We investigate convergence properties in weighted spaces of distributions D′ Lp and their test spaces DLq , 1 p + 1 q = 1. Also we give characterization of weak limits of weakly convergent sequences of L-distributions. AMS Mathematics Subject Classification (2010): 46F05

The problem of the boundedness of the fractional maximal operator Mα, 0 ≤ α < n in local Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters.

For a family of weight functions invariant under a finite reflection group, we show how weighted Lp multiplier theorems for Dunkl transform on the Euclidean space Rd can be transferred from the corresponding results for hharmonic expansions on the unit sphere Sd of Rd+1. The result is then applied to establish a Hörmander type multiplier theorem for the Dunkl transform and to show the convergen...

The main result of this paper is an intersection representation for a class anisotropic vector-valued function spaces in axiomatic setting à la Hedberg and Netrusov (2007), which includes weighted mixed-norm Besov Lizorkin–Triebel spaces. In the special case classical spaces, gives improvement well-known Fubini property. has applications Lq-Lp-maximal regularity problem parabolic boundary value...