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BOUNDEDNESS OF SEVERAL INTEGRAL OPERATORS WITH BOUNDED VARIABLE KERNELS ON HARDY AND WEAK HARDY SPACES

HUA WANG

College of Mathematics and Econometrics, Hunan University, Changsha 410082, P. R. China

https://doi.org/10.1142/S0129167X1350095XCited by:8 (Source: Crossref)

Abstract

In this paper, by using the atomic decomposition theory of Hardy space H¹(ℝⁿ) and weak Hardy space WH¹(ℝⁿ), we give the boundedness properties of some operators with variable kernels such as singular integral operators, fractional integrals and parametric Marcinkiewicz integrals on these spaces, under certain logarithmic type Lipschitz conditions assumed on the variable kernel Ω(x, z).

Keywords:

AMSC: 42B20, 42B25, 42B30

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