### A characterization of ${H}^{p}\left({R}^{n}\right)$ in terms of atoms

Robert Latter (1978)

Studia Mathematica

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Robert Latter (1978)

Studia Mathematica

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Calixto Calderón (1975)

Studia Mathematica

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A. Gatto, Stephen Vági (1992)

Studia Mathematica

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In this paper we prove the continuity of fractional integrals acting on nonhomogeneous function spaces defined on spaces of homogeneous type with finite measure. A definition of the molecules which are used in the ${H}^{p}$ theory is given. Results are proved for ${L}^{p}$, ${H}^{p}$, BMO, and Lipschitz spaces.

Ferenc Weisz (1996)

Studia Mathematica

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The inequality (*) $({\sum}_{\left|n\right|=1}^{\infty}{\sum}_{\left|m\right|=1}^{\infty}{\left|nm\right|}^{p-2}{\left|f\u0302(n,m)\right|}^{p}{)}^{1/p}\le {C}_{p}\parallel \u0192{\parallel}_{{H}_{p}}$ (0 < p ≤ 2) is proved for two-parameter trigonometric-Fourier coefficients and for the two-dimensional classical Hardy space ${H}_{p}$ on the bidisc. The inequality (*) is extended to each p if the Fourier coefficients are monotone. For monotone coefficients and for every p, the supremum of the partial sums of the Fourier series is in ${L}_{p}$ whenever the left hand side of (*) is finite. From this it follows that under the same condition the two-dimensional trigonometric-Fourier...

Ferenc Weisz (1996)

Studia Mathematica

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It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space ${H}_{p,q}$ to ${L}_{p,q}$ (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type $({L}_{1},{L}_{1})$. As a consequence we show that the dyadic integral of a ∞ function $f\in {L}_{1}$ is dyadically differentiable and its derivative is f a.e.

Margaret Murray (1987)

Studia Mathematica

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Daning Chen, Dashan Fan (1998)

Studia Mathematica

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The authors obtain some multiplier theorems on ${H}^{p}$ spaces analogous to the classical ${L}^{p}$ multiplier theorems of de Leeuw. The main result is that a multiplier operator ${\left(Tf\right)}^{(}x)=\lambda \left(x\right)f\u0302\left(x\right)$ $\left(\lambda \in C\left({\mathbb{R}}^{n}\right)\right)$ is bounded on ${H}^{p}\left({\mathbb{R}}^{n}\right)$ if and only if the restriction ${\lambda \left(\epsilon m\right)}_{m\in \Lambda}$ is an ${H}^{p}\left({T}^{n}\right)$ bounded multiplier uniformly for ε>0, where Λ is the integer lattice in ${\mathbb{R}}^{n}$.

Umberto Neri (1975)

Studia Mathematica

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Jürgen Marschall (1987)

Studia Mathematica

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Roberto Macías, Carlos Segovia (1979)

Studia Mathematica

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Calixto Calderón (1979)

Studia Mathematica

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Josefina Alvarez (1998)

Collectanea Mathematica

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