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Martingale Orlicz‐Hardy spaces
Mathematische Nachrichten, 2012AbstractThe purpose of this paper is to introduce five martingale Orlicz‐Hardy spaces and to establish the atomic decomposition theorem. As applications we show the relation among five martingale Orlicz‐Hardy spaces and the duality, namely, the dual of martingale Orlicz‐Hardy spaces are generalized martingale Campanato spaces.
Miyamoto, Takashi +2 more
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Löwner Chains and Hardy Spaces
Bulletin of the London Mathematical Society, 1991Let a family of univalent functions \(f(z,t):\mathbb{D}\to\mathbb{C}\), \(t\geq 0\), be a Löwner chain satisfying \(\dot f(z,t)=zf'(z,t)p(z,t)\) for \(z\) in the unit disc \(\mathbb{D}\), a.e. \(t\geq 0\), where \(p(z,t)\) is analytic for \(z\in\mathbb{D}\) and measurable for \(t\geq 0\) with \({\mathfrak R}[p(z,t)]\geq 0\). The symbols \(\dot f(z,t)\)
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A Remark on Bases in Hardy Spaces
Canadian Mathematical Bulletin, 1984AbstractThe Franklin spline system in [0,1] has been generalized by Strömberg to a system in ℝn which is an unconditional basis in Hp(ℝn) for p > n/(n + m +1). Here the natural number m is the order of the system. For some of these values of p, it was known that the Hp quasi-norm is equivalent to a certain expression containing the coefficients of ...
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1998
In this chapter we study various properties of the spacesH 1 H 2 andH ∞in preparation for our study of Toeplitz operators in the following chapter. Due to the availability of several excellent accounts of this subject (see Notes), we do not attempt a comprehensive treatment and proceed in the main using the techniques which we have already introduced.
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In this chapter we study various properties of the spacesH 1 H 2 andH ∞in preparation for our study of Toeplitz operators in the following chapter. Due to the availability of several excellent accounts of this subject (see Notes), we do not attempt a comprehensive treatment and proceed in the main using the techniques which we have already introduced.
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Hardy Spaces and Beurling Algebras
Journal of the London Mathematical Society, 1989The author introduces the spaces \(A^ p\) and \(B^ p\), which have previously been considered by Chen and Lau on the line, on \({\mathbb{R}}^ n\). Let \(B(x,R)=\{y\in {\mathbb{R}}^ n| | x-y|
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FRAMES OF WAVELETS IN HARDY SPACE
Analysis, 1995Summary: Necessary and sufficient conditions are stated and proved for a system of functions \(\psi_{j,k}(s)= 2^{j/2} \psi(2^j s- k)\), \(j,k\in {\mathbf Z}\), to form a frame of wavelets in the Hardy space \({\mathbf H}^{2+}\). These conditions are expressed in terms of the Fourier transform \(\widehat\psi\) of \(\psi\).
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Canadian Mathematical Bulletin, 1990
AbstractW. Deeb, R. Khalil and M. Marzuq have studied some properties of H(ϕ), the Hardy-Orlicz spaces. They introduced the functions class Np (0 < p ≦ 1 ) and discussed some properties of Np. In the present short note we prove that Np = N+ for 0 < p ≦ 1. We also give a condition of H(ϕ) = H(ψ).
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AbstractW. Deeb, R. Khalil and M. Marzuq have studied some properties of H(ϕ), the Hardy-Orlicz spaces. They introduced the functions class Np (0 < p ≦ 1 ) and discussed some properties of Np. In the present short note we prove that Np = N+ for 0 < p ≦ 1. We also give a condition of H(ϕ) = H(ψ).
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Two characterizations of central BMO space via the commutators of Hardy operators
Forum Mathematicum, 2021Shaoguang Shi, Zunwei Fu
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