Restricted estimates of the fractional integral on the diagonal

Ting Chen and Wenchang Sun

Mathematische Nachrichten, 2023, vol. 296, issue 3, 1013-1024

Abstract: For a function in a mixed‐norm Lebesgue space, we study the restriction of its fractional integral on the diagonal. We show that the restriction is weakly bounded when the indices satisfy certain conditions. We give a complete characterization of such indices. To prove this result, we generalize a classical result on operators that commute with translations.

Date: 2023
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