Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 357-398

MOLECULAR CHARACTERIZATIONS AND DUALITIES OF VARIABLE EXPONENT HARDY SPACES ASSOCIATED WITH OPERATORS

Dachun Yang and Ciqiang Zhuo

Beijing Normal University, School of Mathematical Sciences
Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing 100875, P.R. China; dcyang 'at' bnu.edu.cn

Beijing Normal University, School of Mathematical Sciences
Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing 100875, P.R. China; cqzhuo 'at' mail.bnu.edu.cn

Abstract. Let L be a linear operator on L²(Rⁿ) generating an analytic semigroup {e^-tL}_t≥0 with kernels having pointwise upper bounds and p(⋅) : Rⁿ → (0,1] be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the authors introduce the variable exponent Hardy space associated with the operator L, denoted by H_L^p(⋅)(Rⁿ), and the BMO-type space BMO_p(⋅),L(Rⁿ). By means of tent spaces with variable exponents, the authors then establish the molecular characterization of H_L^p(⋅)(Rⁿ) and a duality theorem between such a Hardy space and a BMO-type space. As applications, the authors study the boundedness of the fractional integral on these Hardy spaces and the coincidence between H_L^p(⋅)(Rⁿ) and the variable exponent Hardy spaces H^p(⋅)(Rⁿ).

2010 Mathematics Subject Classification: Primary 42B35; Secondary 42B30, 35K08, 47D03.

Key words: Hardy space, BMO space, variable exponent, operator, heat kernel, molecule.

Reference to this article: D. Yang and C. Zhuo: Molecular characterizations and dualities of variable exponent Hardy spaces associated with operators. Ann. Acad. Sci. Fenn. Math. 41 (2016), 357-398.

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doi:10.5186/aasfm.2016.4125