Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2513672965', 'doi': 'https://doi.org/10.1002/mana.201500331', 'title': 'On associate spaces of weighted Sobolev space on the real line', 'display_name': 'On associate spaces of weighted Sobolev space on the real line', 'publication_year': 2016, 'publication_date': '2016-08-16', 'ids': {'openalex': 'https://openalex.org/W2513672965', 'doi': 'https://doi.org/10.1002/mana.201500331', 'mag': '2513672965'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/mana.201500331', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S73458468', 'display_name': 'Mathematische Nachrichten', 'issn_l': '0025-584X', 'issn': ['0025-584X', '1522-2616'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5079279918', 'display_name': 'Д. В. Прохоров', 'orcid': 'https://orcid.org/0000-0003-1802-6121'}, 'institutions': [{'id': 'https://openalex.org/I4210143490', 'display_name': 'Computing Center', 'ror': 'https://ror.org/0557kgc34', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I1313323035', 'https://openalex.org/I4210143490', 'https://openalex.org/I4210148470']}, {'id': 'https://openalex.org/I1313323035', 'display_name': 'Russian Academy of Sciences', 'ror': 'https://ror.org/05qrfxd25', 'country_code': 'RU', 'type': 'government', 'lineage': ['https://openalex.org/I1313323035']}, {'id': 'https://openalex.org/I2801160905', 'display_name': 'Steklov Mathematical Institute', 'ror': 'https://ror.org/03zeg8w71', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I1313323035', 'https://openalex.org/I2801160905', 'https://openalex.org/I4210124601']}], 'countries': ['RU'], 'is_corresponding': True, 'raw_author_name': 'Dmitrii V. Prokhorov', 'raw_affiliation_strings': ['Computing Center of Far Eastern Branch of Russian Academy of Sciences, Kim Yu Chena 65, 680000 Khabarovsk, Russia', 'Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia'], 'affiliations': [{'raw_affiliation_string': 'Computing Center of Far Eastern Branch of Russian Academy of Sciences, Kim Yu Chena 65, 680000 Khabarovsk, Russia', 'institution_ids': ['https://openalex.org/I4210143490', 'https://openalex.org/I1313323035']}, {'raw_affiliation_string': 'Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia', 'institution_ids': ['https://openalex.org/I2801160905', 'https://openalex.org/I1313323035']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5083486743', 'display_name': 'В. Д. Степанов', 'orcid': 'https://orcid.org/0000-0002-6760-9019'}, 'institutions': [{'id': 'https://openalex.org/I2801160905', 'display_name': 'Steklov Mathematical Institute', 'ror': 'https://ror.org/03zeg8w71', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I1313323035', 'https://openalex.org/I2801160905', 'https://openalex.org/I4210124601']}, {'id': 'https://openalex.org/I1313323035', 'display_name': 'Russian Academy of Sciences', 'ror': 'https://ror.org/05qrfxd25', 'country_code': 'RU', 'type': 'government', 'lineage': ['https://openalex.org/I1313323035']}, {'id': 'https://openalex.org/I126527374', 'display_name': "Peoples' Friendship University of Russia", 'ror': 'https://ror.org/02dn9h927', 'country_code': 'RU', 'type': 'education', 'lineage': ['https://openalex.org/I126527374']}], 'countries': ['RU'], 'is_corresponding': True, 'raw_author_name': 'Vladimir D. Stepanov', 'raw_affiliation_strings': ['Department of Nonlinear Analysis and Optimization, Peoples Friendship University of Russia, Miklukho-Maklay 6, 117198 Moscow, Russia', 'Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia'], 'affiliations': [{'raw_affiliation_string': 'Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia', 'institution_ids': ['https://openalex.org/I2801160905', 'https://openalex.org/I1313323035']}, {'raw_affiliation_string': 'Department of Nonlinear Analysis and Optimization, Peoples Friendship University of Russia, Miklukho-Maklay 6, 117198 Moscow, Russia', 'institution_ids': ['https://openalex.org/I126527374']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5050359666', 'display_name': 'Elena P. Ushakova', 'orcid': 'https://orcid.org/0000-0002-3497-3762'}, 'institutions': [{'id': 'https://openalex.org/I4210143490', 'display_name': 'Computing Center', 'ror': 'https://ror.org/0557kgc34', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I1313323035', 'https://openalex.org/I4210143490', 'https://openalex.org/I4210148470']}, {'id': 'https://openalex.org/I1313323035', 'display_name': 'Russian Academy of Sciences', 'ror': 'https://ror.org/05qrfxd25', 'country_code': 'RU', 'type': 'government', 'lineage': ['https://openalex.org/I1313323035']}, {'id': 'https://openalex.org/I2801160905', 'display_name': 'Steklov Mathematical Institute', 'ror': 'https://ror.org/03zeg8w71', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I1313323035', 'https://openalex.org/I2801160905', 'https://openalex.org/I4210124601']}], 'countries': ['RU'], 'is_corresponding': True, 'raw_author_name': 'Elena P. Ushakova', 'raw_affiliation_strings': ['Computing Center of Far Eastern Branch of Russian Academy of Sciences, Kim Yu Chena 65, 680000 Khabarovsk, Russia', 'Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia'], 'affiliations': [{'raw_affiliation_string': 'Computing Center of Far Eastern Branch of Russian Academy of Sciences, Kim Yu Chena 65, 680000 Khabarovsk, Russia', 'institution_ids': ['https://openalex.org/I4210143490', 'https://openalex.org/I1313323035']}, {'raw_affiliation_string': 'Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina 8, 119991 Moscow, Russia', 'institution_ids': ['https://openalex.org/I2801160905', 'https://openalex.org/I1313323035']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 4, 'corresponding_author_ids': ['https://openalex.org/A5079279918', 'https://openalex.org/A5083486743', 'https://openalex.org/A5050359666'], 'corresponding_institution_ids': ['https://openalex.org/I4210143490', 'https://openalex.org/I1313323035', 'https://openalex.org/I2801160905', 'https://openalex.org/I2801160905', 'https://openalex.org/I1313323035', 'https://openalex.org/I126527374', 'https://openalex.org/I4210143490', 'https://openalex.org/I1313323035', 'https://openalex.org/I2801160905'], 'apc_list': {'value': 3140, 'currency': 'USD', 'value_usd': 3140, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 1.972, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 14, 'citation_normalized_percentile': {'value': 0.74003, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 89, 'max': 90}, 'biblio': {'volume': '290', 'issue': '5-6', 'first_page': '890', 'last_page': '912'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11022', 'display_name': 'Spectral Theory of Differential Operators', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11022', 'display_name': 'Spectral Theory of Differential Operators', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11654', 'display_name': 'Global Well-Posedness of Nonlinear Wave Equations', 'score': 0.9976, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T11049', 'display_name': 'Harmonic Analysis and Operator Theory', 'score': 0.9966, 'subfield': {'id': 'https://openalex.org/subfields/2604', 'display_name': 'Applied Mathematics'}, 'field': {'id': 'https://openalex.org/fields/26', 'display_name': 'Mathematics'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/real-line', 'display_name': 'Real line', 'score': 0.7627547}, {'id': 'https://openalex.org/keywords/line', 'display_name': 'Line (geometry)', 'score': 0.616737}, {'id': 'https://openalex.org/keywords/birnbaum–orlicz-space', 'display_name': 'Birnbaum–Orlicz space', 'score': 0.49769905}, {'id': 'https://openalex.org/keywords/weighted-estimates', 'display_name': 'Weighted Estimates', 'score': 0.466949}, {'id': 'https://openalex.org/keywords/sobolev-inequality', 'display_name': 'Sobolev inequality', 'score': 0.45356342}], 'concepts': [{'id': 'https://openalex.org/C99730327', 'wikidata': 'https://www.wikidata.org/wiki/Q1501536', 'display_name': 'Sobolev space', 'level': 2, 'score': 0.91134757}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8476205}, {'id': 'https://openalex.org/C6183050', 'wikidata': 'https://www.wikidata.org/wiki/Q3058180', 'display_name': 'Interpolation space', 'level': 4, 'score': 0.7808806}, {'id': 'https://openalex.org/C75432250', 'wikidata': 'https://www.wikidata.org/wiki/Q29654355', 'display_name': 'Real line', 'level': 2, 'score': 0.7627547}, {'id': 'https://openalex.org/C198352243', 'wikidata': 'https://www.wikidata.org/wiki/Q37105', 'display_name': 'Line (geometry)', 'level': 2, 'score': 0.616737}, {'id': 'https://openalex.org/C2778572836', 'wikidata': 'https://www.wikidata.org/wiki/Q380933', 'display_name': 'Space (punctuation)', 'level': 2, 'score': 0.56701314}, {'id': 'https://openalex.org/C169976997', 'wikidata': 'https://www.wikidata.org/wiki/Q3058185', 'display_name': 'Birnbaum–Orlicz space', 'level': 5, 'score': 0.49769905}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.4567782}, {'id': 'https://openalex.org/C185644265', 'wikidata': 'https://www.wikidata.org/wiki/Q3711848', 'display_name': 'Sobolev inequality', 'level': 3, 'score': 0.45356342}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.26275536}, {'id': 'https://openalex.org/C55112680', 'wikidata': 'https://www.wikidata.org/wiki/Q190549', 'display_name': 'Functional analysis', 'level': 3, 'score': 0.22669187}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.09831062}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.07915622}, {'id': 'https://openalex.org/C55493867', 'wikidata': 'https://www.wikidata.org/wiki/Q7094', 'display_name': 'Biochemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C104317684', 'wikidata': 'https://www.wikidata.org/wiki/Q7187', 'display_name': 'Gene', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C111919701', 'wikidata': 'https://www.wikidata.org/wiki/Q9135', 'display_name': 'Operating system', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1002/mana.201500331', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S73458468', 'display_name': 'Mathematische Nachrichten', 'issn_l': '0025-584X', 'issn': ['0025-584X', '1522-2616'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320595', 'host_organization_name': 'Wiley', 'host_organization_lineage': ['https://openalex.org/P4310320595'], 'host_organization_lineage_names': ['Wiley'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [{'display_name': 'Reduced inequalities', 'id': 'https://metadata.un.org/sdg/10', 'score': 0.5}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 10, 'referenced_works': ['https://openalex.org/W1499500817', 'https://openalex.org/W1667100528', 'https://openalex.org/W1905935129', 'https://openalex.org/W1993264666', 'https://openalex.org/W2043798737', 'https://openalex.org/W2105040356', 'https://openalex.org/W2123486524', 'https://openalex.org/W2498149293', 'https://openalex.org/W4213354557', 'https://openalex.org/W92076289'], 'related_works': ['https://openalex.org/W4319988904', 'https://openalex.org/W4287815684', 'https://openalex.org/W4241943978', 'https://openalex.org/W3015352488', 'https://openalex.org/W2997765005', 'https://openalex.org/W2963125940', 'https://openalex.org/W266838890', 'https://openalex.org/W2324780684', 'https://openalex.org/W2024928790', 'https://openalex.org/W1963867244'], 'abstract_inverted_index': {'Precise': [0], 'descriptions': [1], 'of': [2], 'the': [3, 11], 'spaces': [4, 9], 'associated': [5], 'with': [6], 'weighted': [7], 'Sobolev': [8], 'on': [10], 'real': [12], 'line': [13], 'are': [14], 'given.': [15]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2513672965', 'counts_by_year': [{'year': 2023, 'cited_by_count': 2}, {'year': 2022, 'cited_by_count': 4}, {'year': 2021, 'cited_by_count': 2}, {'year': 2019, 'cited_by_count': 4}, {'year': 2018, 'cited_by_count': 2}], 'updated_date': '2024-08-21T18:53:46.198622', 'created_date': '2016-09-16'}