Kyoto Journal of Mathematics
- Kyoto J. Math.
- Volume 56, Number 1 (2016), 97-124.
Vector-valued operators with singular kernel and Triebel–Lizorkin block spaces with variable exponents
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.
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
Permanent link to this document
Digital Object Identifier
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]
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