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International Journal of Theoretical Physics, 2003
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Acta Mathematica Sinica, English Series, 2010
As is known, there are various ways to define Hardy spaces, especially in the multi-dimensional setting. One of such approaches is the maximal function approach. Using it, the authors introduce a family of Hardy spaces based on a functional parameter. Many known Hardy and Hardy-Lorentz type spaces are particular cases.
Almeida, Alexandre, Caetano, António M.
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As is known, there are various ways to define Hardy spaces, especially in the multi-dimensional setting. One of such approaches is the maximal function approach. Using it, the authors introduce a family of Hardy spaces based on a functional parameter. Many known Hardy and Hardy-Lorentz type spaces are particular cases.
Almeida, Alexandre, Caetano, António M.
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1992
In Chapter 1 we defined the Poisson integral of a function f ∈ C(S) to be the function P[f] defined on B by $$P\left[ f \right](x) = \int_S {P\left( {x,\zeta } \right)f} \left( \zeta \right)d\sigma \left( \zeta \right)$$ (6.1) .
Sheldon Axler, Paul Bourdon, Wade Ramey
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In Chapter 1 we defined the Poisson integral of a function f ∈ C(S) to be the function P[f] defined on B by $$P\left[ f \right](x) = \int_S {P\left( {x,\zeta } \right)f} \left( \zeta \right)d\sigma \left( \zeta \right)$$ (6.1) .
Sheldon Axler, Paul Bourdon, Wade Ramey
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Analysis Mathematica, 1994
This paper extends a previous one [ibid. 16, No. 3, 227-239 (1990; Zbl 0708.60039)] by the same author. In the setting of a probability space \((\Omega, A, \mathbb{P})\) with an arbitrarily indexed family of sub-\(\sigma\)- fields \(\{F_ t\}_{t \in T}\), the concept of atomic Hardy spaces \(H^ q\), \(q \in (1,\infty]\), in the spirit of \textit{R.
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This paper extends a previous one [ibid. 16, No. 3, 227-239 (1990; Zbl 0708.60039)] by the same author. In the setting of a probability space \((\Omega, A, \mathbb{P})\) with an arbitrarily indexed family of sub-\(\sigma\)- fields \(\{F_ t\}_{t \in T}\), the concept of atomic Hardy spaces \(H^ q\), \(q \in (1,\infty]\), in the spirit of \textit{R.
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Two characterizations of central BMO space via the commutators of Hardy operators
Forum Mathematicum, 2021Zunwei Fu, Shaoguang Shi
exaly
Studia Mathematica, 1998
We study various characterizations of the Hardy spaces Hp(ℤ) via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of Hp(ℤ) given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
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We study various characterizations of the Hardy spaces Hp(ℤ) via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of Hp(ℤ) given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
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