Dunyan Yan

Singular integrals and related topics

Hardy-Littlewood Maxial Operator Singular Integral Operators Fractional Integral Operators Oscillatory Singular Integrals Littlewood-Paley Operator.

The Bedrosian identity for the Hilbert transform of product functions

We investigate a necessary and sufficient condition which ensures validity of the Bedrosian identity for the Hilbert transform of a product function fg. Convenient sufficient conditions are presented, which cover the classical Bedrosian theorem and provide us with new insightful information.

Fourier spectrum characterization of Hardy spaces and applications

We characterize in terms of Fourier spectrum the boundary values of functions in the complex Hardy spaces H P (C ± ), 1 < p < oo. As an application we extend the Bedrosian identity, originally stated for square-integrable functions, to the L P (R) cases.

On the commutator of the Marcinkiewicz integral

Abstract L p ( R n ) boundedness is considered for the commutator of higher-dimensional Marcinkiewicz integral. Some conditions implying the L 2 ( R n ) and the L p ( R n ) boundedness for the commutator of the Marcinkiewicz integral are obtained.

Characterizations of multi-knot piecewise linear spectral sequences

We study two classes of orthonormal bases for

On The Multilinear Fractional Integral Operators With Correlation Kernels

L^{2} {\left[ {0,1} \right]}

HARDY-LITTLEWOOD MAXIMAL OPERATOR

in this paper. The exponential parts of these bases are multi-knot piecewise linear functions. These bases are called spectral sequences. Characterizations of these multi-knot piecewise linear functions are provided. We also consider an opposite problem for single-knot piecewise linear spectral sequences, where the piecewise linear functions are defined on