Title: Fractional integration along homogeneous curves in $R^3$
Abstract:1 p y 1 q <e Q where Q is the homogeneous dimension of R with respect to the dilations (3). If 2 R, another necessary condition on p and q is due to the fact that T dominates the operator T0 w...1 p y 1 q <e Q where Q is the homogeneous dimension of R with respect to the dilations (3). If 2 R, another necessary condition on p and q is due to the fact that T dominates the operator T0 which is defined by limiting the integration in (2) to a bounded interval of R which doesn't contain the origin. According to what has been proved in [3] and later improved in [4], T0 is bounded from Lp R3 to Lq R3 when p ; q belongs to the closed trapezoid with vertices A 0; 0; B 1; 1; C 3 ; 2; D 2 ; 3. As we will prove, this condition is also necessary when 2 C. MATH. SCAND. 85 (1999), 259^270Read More