Hardy spaces for a class of singular domains

p-Carleson Measures for a Class of Hardy-Orlicz Spaces

An alternative interpretation of a family of weighted Carleson measures is used to characterize p-Carleson measures for a class of Hardy-Orlicz spaces admitting a nice weak factorization. As an application, we provide with a characterization of symbols of bounded weighted composition operators and Cesàro-type integral operators from these Hardy-Orlicz spaces to some classical holomorphic functi...

A new class of function spaces on domains of R^d and its relations to classical function spaces

Boundedness of Singular Integrals in Weighted Anisotropic Product Hardy Spaces

Let Ai for i = 1, 2 be an expansive dilation, respectively, on R n and R and ~ A ≡ (A1, A2). Denote by A∞(R × R; ~ A) the class of Muckenhoupt weights associated with ~ A. The authors introduce a class of anisotropic singular integrals on R×R, whose kernels are adapted to ~ A in the sense of Bownik and have vanishing moments defined via bump functions in the sense of Stein. Then the authors est...

Weighted Hardy and singular operators in Morrey spaces

We study the weighted boundedness of the Cauchy singular integral operator SΓ in Morrey spaces L(Γ) on curves satisfying the arc-chord condition, for a class of ”radial type” almost monotonic weights. The non-weighted boundedness is shown to hold on an arbitrary Carleson curve. We show that the weighted boundedness is reduced to the boundedness of weighted Hardy operators in Morrey spaces L(0, ...

$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...