Kyoto Journal of Mathematics

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

Kwok-Pun Ho

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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.

Article information

Source
Kyoto J. Math., Volume 56, Number 1 (2016), 97-124.

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

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1458047879

Digital Object Identifier
doi:10.1215/21562261-3445165

Mathematical Reviews number (MathSciNet)
MR3479319

Zentralblatt MATH identifier
1361.42024

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 47B38: Operators on function spaces (general) 47G10: Integral operators [See also 45P05]

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

Citation

Ho, Kwok-Pun. Vector-valued operators with singular kernel and Triebel–Lizorkin block spaces with variable exponents. Kyoto J. Math. 56 (2016), no. 1, 97--124. doi:10.1215/21562261-3445165. https://projecteuclid.org/euclid.kjm/1458047879


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