A new proof of a weighted norm inequality for multilinear singular integrals of Calderón-Zygmund type is presented through a more general estimate involving a sharp maximal function. An application is given to the study of certain multilinear commutators.

Optimal sufficient conditions are found in weighted Lorentz spaces for weight functions which provide the boundedness of the Calderón– Zygmund singular integral operator defined on spaces of homogeneous and nonhomogeneous type. 2000 Mathematics Subject Classification: 42B20, 42B25.

Abstract We prove stronger variants of a multiplier theorem Kislyakov. The key ingredients are based on ideas Kislyakov and the Kahane–Salem–Zygmund inequality. As by-product, we show various theorems for spaces trigonometric polynomials n -dimensional torus $\mathbb {T}^n$ or Boolean cubes $\{-1,1\}^N$ . Our more abstract approach local Banach space theory has advantage that it allows to consi...

The boundedness and the compactness of generalized weighted composition operators from weighted Bergman spaces into Zygmund-type spaces are investigated in this paper. Moreover, we give some estimates for the essential norm of these operators.

In this paper we extend a Calderón-Zygmund commutator-type estimate. This estimate enables us to prove an embedding result concerning weighted function spaces. 2000 Mathematics Subject Classification: 42B15, 42B20, 42B25, 42B35.

In this work, we continue the study of precise functional properties of a linear operator linked with Boltzmann quadratic operator, started in Part I. This is done for singular cross-sections. In particular, we show Calderon-Zygmund type estimates.

On some probability space (Ω,F,P), we consider two independent sequences (ak)k≥1 and (bk)k≥1 of i.i.d. random variables that are centered with unit variance which admit a moment strictly higher than two. We then the associated trigonometric polynomial fn(t):=1 n ∑k=1nakcos(kt)+bksin(kt), t∈R. In their seminal work, for Rademacher coefficients, Salem Zygmund showed P almost surely: ∀t∈R,1 2π∫02π...

We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.

In this paper we obtain some limit cases of inequalities of Ul’yanov-type for modulus of smoothness between Lorentz-Zygmund spaces on Tn . Corresponding embedding theorems for the Besov spaces are investigated. Mathematics subject classification (2010): 41A17, 46E30, 46E35, 46M35.

We prove that certain boundedness properties of operators yield distributional estimates that have exponential decay at infinity. Such distributional estimates imply local exponential integrability and apply to many operators such as m-linear Calderón-Zygmund operators and their maximal counterparts.