Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 31-62

ATOMIC DECOMPOSITION OF HARDY–MORREY SPACES WITH VARIABLE EXPONENTS

Kwok-Pun Ho

The Hong Kong Institute of Education, Department of Mathematics and Information Technology
10, Lo Ping Road, Tai Po, Hong Kong, P.R. China; vkpho 'at' ied.edu.hk

Abstract. The Hardy–Morrey spaces with variable exponents are introduced in terms of maximal functions. The atomic decomposition of Hardy–Morrey spaces with variable exponents is established. This decomposition extends and unifies several atomic decompositions of Hardy type spaces such as the Hardy–Morrey spaces and the Hardy spaces with variable exponents. Some applications of this atomic decomposition on singular integral are presented.

2010 Mathematics Subject Classification: Primary 42B20, 42B25, 42B35, 46E30.

Key words: Atomic decomposition, Morrey spaces, Hardy spaces, maximal functions, variable exponent analysis, vector-valued maximal inequalities.

Reference to this article: K.-P. Ho: Atomic decomposition of Hardy–Morrey spaces with variable exponents. Ann. Acad. Sci. Fenn. Math. 40 (2015), 31-62.

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doi:10.5186/aasfm.2015.4002