Potentials with product kernels in grand Lebesgue spaces: One-weight criteria(*)

作者：Kokilashvili Vakhtang^*; Meskhi Alexander

来源：Lithuanian Mathematical Journal, 2013, 53(1): 27-39.

DOI：10.1007/s10986-013-9191-y

• grand Lebesgue spaces
• strong fractional maximal operator
• potentials with product kernels
• weights
• boundedness
• one-weight inequality

We study the boundedness problem for fractional integral operators with product kernels and corresponding strong fractional maximal operators in unweighted and weighted grand Lebesgue spaces. Among other statements, we prove that the one-weight inequality , where q is the Hardy-Littlewood-Sobolev exponent of p, holds for potentials with product kernels T (alpha) if and only if the weight w belongs to the Muckenhoupt class A (1+q/p') defined with respect to n-dimensional intervals with sides parallel to the coordinate axes. We also provide a motivation of choosing theta q/p as the second parameter of the target space.

• 出版日期2013-1