Vector-valued operators with singular kernel and Triebel–Lizorkin block spaces with variable exponents

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20 Citations (Scopus)

Abstract

We establish two principles which state that, whenever an operator is bounded on a given Banach function space, then under some simple conditions, it is also bounded on the corresponding Morrey spaces and block spaces. By applying these principles on some concrete operators, we generalize the Fefferman-Stein vector-valued inequalities, define and study theTriebel-Lizorkin block spaces with variable exponents, and extend the mapping properties of the fractional integral operators to Morrey-type spaces and block-type spaces. Copyright © 2016 by Kyoto University.
Original languageEnglish
Pages (from-to)97-124
JournalKyoto Journal of Mathematics
Volume56
Issue number1
DOIs
Publication statusPublished - 2016

Citation

Ho, K.-P. (2016). Vector-valued operators with singular kernel and Triebel–Lizorkin block spaces with variable exponents. Kyoto Journal of Mathematics, 56(1), 97-124.

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