Open Access
April 2016 Vector-valued operators with singular kernel and Triebel–Lizorkin block spaces with variable exponents
Kwok-Pun Ho
Kyoto J. Math. 56(1): 97-124 (April 2016). DOI: 10.1215/21562261-3445165

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 the Triebel–Lizorkin block spaces with variable exponents, and extend the mapping properties of the fractional integral operators to Morrey-type spaces and block-type spaces.

Citation

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Kwok-Pun Ho. "Vector-valued operators with singular kernel and Triebel–Lizorkin block spaces with variable exponents." Kyoto J. Math. 56 (1) 97 - 124, April 2016. https://doi.org/10.1215/21562261-3445165

Information

Received: 29 September 2014; Revised: 16 December 2014; Accepted: 16 December 2014; Published: April 2016
First available in Project Euclid: 15 March 2016

zbMATH: 1361.42024
MathSciNet: MR3479319
Digital Object Identifier: 10.1215/21562261-3445165

Subjects:
Primary: 42B20 , 42B25
Secondary: 47B38 , 47G10

Keywords: Block spaces , fractional integral operators , Hardy–Littlewood maximal operator , Morrey spaces , singular integral operators , Triebel–Lizorkin spaces , variable exponent analysis

Rights: Copyright © 2016 Kyoto University

Vol.56 • No. 1 • April 2016
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