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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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


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.

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