Title: Parabolic maximal functions associated with a distribution, II
Abstract: In this article we continue with the study, which we initiated in [3], of the classes H v of distributions in R n. Section 1 of this paper deals with the question of finding a convenient dense class of functions in H v, and the closely associated spaces/~q, 0 < q < 1. Section 2 describes the dual spaces of the H~ classes, 0 < p ~ 1. For the classes H ~ of analytic functions in the disc this is done in [5], when 0 < p ~ 1 ; and for H 1 in a half space and the so-called elliptic case, this is of course one of the celebrated results of [7]. Section 3 constructs the intermediate interpolation spaces, both by the complex method and by the real K method of Peetre, of the spaces H ~ and/ t~ . The real method, as it applies to the elliptic H ~ spaces, is given in [6]. Section 4 is devoted to the study of multipliers and fractional integrals acting in H ~ spaces. In the elliptic case, Theorem 4.7 is similar to a known result which can be found in [10, 11]. The reading of this paper will require some familiarity wkh the concepts introduced, and the results proved in [3]. We shall use the same notation and we just remark that the letter c will denote a constant, which need not be the same in different occurrences.