All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 9 of 9

Showing per page

Painlevé null sets, dimension and compact embedding of weighted holomorphic spaces

Alexander V. Abanin, Pham Trong Tien (2012)

Studia Mathematica

We obtain, in terms of associated weights, natural criteria for compact embedding of weighted Banach spaces of holomorphic functions on a wide class of domains in the complex plane. Our study is based on a complete characterization of finite-dimensional weighted spaces and canonical weights for them. In particular, we show that for a domain whose complement is not a Painlevé null set each nontrivial space of holomorphic functions with O-growth condition is infinite-dimensional.

Pointwise inequalities of logarithmic type in Hardy-Hölder spaces

Slim Chaabane, Imed Feki (2014)

Czechoslovak Mathematical Journal

We prove some optimal logarithmic estimates in the Hardy space H ∞ ( G ) with Hölder regularity, where G is the open unit disk or an annular domain of ℂ . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space H k , ∞ of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem...

Polyanalytic Besov spaces and approximation by dilatations

Ali Abkar (2024)

Czechoslovak Mathematical Journal

Using partial derivatives ∂ f / ∂ z and ∂ f / ∂ z ¯ , we introduce Besov spaces of polyanalytic functions in the open unit disk, as well as in the upper half-plane. We then prove that the dilatations of functions in certain weighted polyanalytic Besov spaces converge to the same functions in norm. When restricted to the open unit disk, we prove that each polyanalytic function of degree q can be approximated in norm by polyanalytic polynomials of degree at most q .

Products of Toeplitz operators and Hankel operators

Yufeng Lu, Linghui Kong (2014)

Studia Mathematica

We first determine when the sum of products of Hankel and Toeplitz operators is equal to zero; then we characterize when the product of a Toeplitz operator and a Hankel operator is a compact perturbation of a Hankel operator or a Toeplitz operator and when it is a finite rank perturbation of a Toeplitz operator.

Properties of harmonic conjugates

Paweł Sobolewski (2008)

Annales UMCS, Mathematica

We give a new proof of Hardy and Littlewood theorem concerning harmonic conjugates of functions u such that ∫D |u(z)|pdA(z) < ∞, 0 < p ≤ 1. We also obtain an inequality for integral means of such harmonic functions u.

Currently displaying 1 – 9 of 9

Page 1