A real variable characterization of $H^{p}$

Ronald Coifman

Displaying similar documents to “A real variable characterization of $H^{p}$ ”

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

Robert Latter (1978)

Studia Mathematica

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On commutators of singular integrals

Calixto Calderón (1975)

Studia Mathematica

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On molecules and fractional integrals on spaces of homogeneous type with finite measure

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.

Two-parameter Hardy-Littlewood inequalities

Ferenc Weisz (1996)

Studia Mathematica

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The inequality (*) $(\sum_{| n | = 1}^{\infty} \sum_{| m | = 1}^{\infty} {| n m |}^{p - 2} {| f ̂ (n, m) |}^{p})^{1 / p} \leq C_{p} ∥ ƒ ∥_{H_{p}}$ (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...

$(H_{p}, L_{p})$ -type inequalities for the two-dimensional dyadic derivative

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.

Multilinear singular integrals involving a derivative of fractional order

Margaret Murray (1987)

Studia Mathematica

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Multiplier transformations on $H^{p}$ spaces

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 ${(T f)}^{(} x) = λ (x) f ̂ (x)$ $(λ \in C (ℝ^{n}))$ is bounded on $H^{p} (ℝ^{n})$ if and only if the restriction ${λ (ε m)}_{m \in Λ}$ is an $H^{p} (T^{n})$ bounded multiplier uniformly for ε>0, where Λ is the integer lattice in $ℝ^{n}$ .