Hardy Spaces Generated by an Integrability Condition
نویسنده
چکیده
S. A. Telyakovskiı̆ (1964, Izv. Akad. Nauk. SSR. Ser. Mat. 28, 1209–1236) proved an integrability condition for cosine series. No condition superior to that has been given so far. In this paper we identify the atomic structure of the Hardy type space that can be associated with this condition. As a consequence, we conclude that Telyakovskiı̆’s condition is equivalent to certain Sidon type inequalities. Then on the basis of this equivalence we show how the atomic technique can be used to extend Telyakovskiı̆’s condition to several systems, including Walsh series and integrals, in a uniform way. © 2001 Academic Press
منابع مشابه
Composition Operators That Improve Integrability on Weighted Bergman Spaces
Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.
متن کامل$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...
متن کاملHankel Operators between Hardy-orlicz Spaces and Products of Holomorphic Functions
For Bn the unit ball of Cn, we consider Hardy-Orlicz spaces of holomorphic functions H, which are preduals of spaces of BMOA type with weight. We characterize the symbols of Hankel operators that extend into bounded operators from the Hardy-Orlicz H1 into H2 . We also consider the closely related question of integrability properties of the product of two functions, one in H1 and the other one i...
متن کاملExtension of Hardy Inequality on Weighted Sequence Spaces
Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...
متن کامل0 Ja n 20 02 Hardy spaces and divergence operators on strongly Lipschitz domains
Let Ω be a strongly Lipschitz domain of Rn. Consider an elliptic second order divergence operator L (including a boundary condition on ∂Ω) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function f via the Poisson semigroup for L to be in L1. Under suitable assumptions on L, we identify this maximal Hardy space with atomic Hardy spaces, namely with...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Journal of Approximation Theory
دوره 113 شماره
صفحات -
تاریخ انتشار 2001