Function spaces play a significant role in harmonic analysis and partial differential equations. The integral operators that form a bridge between function spaces and partial differential equations are the Calderón-Zygmund operators. It is well known that Calderón-Zygmund operators are bounded on the Lebesgue space L(R) for 1 < p < ∞. It is also known that the Calderón-Zygmund operators are not...

In this work, we present a bilinear Tb theorem for singular integral operators of Calderón-Zygmund type. We prove some new accretive type Littlewood-Paley results and construct a bilinear paraproduct for a para-accretive function setting. As an application of our bilinear Tb theorem, we prove product Lebesgue space bounds for bilinear Riesz transforms defined on Lipschitz curves.

The aim of this paper is to investigate the boundedness and compactness Stevic-Sharma operator T?1,?2,? from QK(p, q) QK,0(p,q) spaces Zygmund-type space little space. We also give upper lower estimations for norm T?1,?2,?.

Given a weight , we consider the space ML which coincides with L p when ∈ Ap . Sharp weighted norm inequalities on ML for the Calderón–Zygmund and Littlewood–Paley operators are obtained in terms of the Ap characteristic of for any 1<p<∞. © 2005 Elsevier Inc. All rights reserved.

For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted L space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding o...

In this paper, we obtain the results on degree of convergence a function Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund \begin{document}$ (D^{h}_{g}N^{a,b}) $\end{document} transformation. Important corollaries are deduced from our main results. Some applications als...

An optimal decomposition formula for the norm in the Orlicz space L(log L) is given. New proofs of some results involving L(log L) spaces are given and the decomposition is applied to apriori estimates for elliptic partial differential equations with the right-hand side in Zygmund classes. 2000 Mathematics Subject Classification: 46E35, 46E39, 35J05.

We prove estimates of Calderón-Zygmund type for evolutionary pLaplacian systems in the setting of Lorentz spaces. We suppose the coefficients of the system to satisfy only a VMO condition with respect to the space variable. Our results hold true, mutatis mutandis, also for stationary p-Laplacian systems. PUBLISHED IN J. Differential Equations 255 (9): 2927–2951, 2013

Let g be a holomorphic function of the unit ball B in the ndimensional space, and denote by Tg and Ig the induced extended Cesáro operator and another integral operator. The boundedness and compactness of Tg and Ig acting on the Zygmund spaces in the unit ball are discussed and necessary and sufficient conditions are given in this paper.