Hokkaido Mathematical Journal

A new generalization of Besov-type and Triebel-Lizorkin-type spaces and wavelets

Koichi SAKA

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Abstract

In this paper we introduce a new function space which unifies and generalizes the Besov-type and the Triebel-Lizorkin-type function spaces introduced by S. Jaffard and D. Yang- W. Yuan. This new function space covers the Besov spaces and the Triebel-Lizorkin spaces in the homogeneous case, and further the Morrey spaces. We define the new function space through wavelet expansions. We establish characterizations of the new function space such as the ϕ-transform characterization in the sense of Frazier-Jawerth, the atomic and molecular decomposition characterization. Moreover, in the inhomogeneous case, we give a characterization by local polynomial approximation. As application, we investigate the boundedness of the Calderòn-Zygmund operator and the trace theorem on the new function space.

Article information

Source
Hokkaido Math. J., Volume 40, Number 1 (2011), 111-147.

Dates
First available in Project Euclid: 14 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1300108402

Digital Object Identifier
doi:10.14492/hokmj/1300108402

Mathematical Reviews number (MathSciNet)
MR2790833

Zentralblatt MATH identifier
1221.42044

Subjects
Primary: 42B35: Function spaces arising in harmonic analysis 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42C40: Wavelets and other special systems

Keywords
wavelet Besov space Triebel-Lizorkin space trace theorem Calderon-Zygmund operator atomic and molecular decomposition

Citation

SAKA, Koichi. A new generalization of Besov-type and Triebel-Lizorkin-type spaces and wavelets. Hokkaido Math. J. 40 (2011), no. 1, 111--147. doi:10.14492/hokmj/1300108402. https://projecteuclid.org/euclid.hokmj/1300108402


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