Approximation in Hardy spaces

Journal of the London Mathematical Society, 1998

Hacettepe Journal of Mathematics and Statistics, 2017

We introduce new spaces that are extensions of the Hardy spaces and prove a removable singularity result for holomorphic functions within these spaces. Additionally we provide non-trivial examples.

Monatshefte Fur Mathematik, 1993

We study the geometry of plane domains and the uniform Hölder continuity properties of analytic functions.

Lecture Notes in Mathematics, 1989

Previous chapters were preliminary in the sense that they covered some of the basic results leading to the theory of the weighted Hardy spaces. Another important property, namely, the fact that the "norm" of a distribution in these spaces can be computed in various equivalent ways, is the content of this chapter.

Transactions of the American Mathematical …, 1978

Let f{z) = J,fanz" be close-to-convex on the unit disc. It is shown that (a) if A > 0, then/ belongs to the Hardy space Hx if and only if 2 «x"2|a"|x is finite and that (b) if 0 < X < 1, then/' G Hx if and only if either 2 na_2|ajx or, equivalently, fl0Mx(r,f')dr is convergent. It is noted that the first of these results does not extend to the full class of univalent functions and that the second is best possible in a number of different senses.

Journal of Functional Analysis, 1991

We present some inequalities for the Taylor coefficients of a Hardy-Orlicz function, which in the case of the standard Hardy spaces reduce to the inequalities of Hardy and Littlewood. The proofs are new and elementary even in the case of the classical Hardy spaces. We also prove a Marcinkiewicz type theorem that extends a theorem of Kislyakov and Xu. At the end, we prove a Hardy-Prawitz criterion for membership of a univalent function in a Hardy-Orlicz space.

Journal of the Mathematical Society of Japan, 1990

2009

Hardy spaces with generalized parameter are introduced following the maximal characterization approach. As particular cases, they include the classical H p spaces and the Hardy-Lorentz spaces H p,q . Real interpolation results with function parameter are obtained. Based on them, the behavior of some classical operators is studied in this generalized setting.