Restrictions from $ℝ^{n}$ to $ℤ^{n}$ of weak type (1,1) multipliers

Nakhlé Asmar; Earl Berkson; Jean Bourgain

Displaying similar documents to “Restrictions from $ℝ^{n}$ to $ℤ^{n}$ of weak type (1,1) multipliers”

Weak type (1,1) multipliers on LCA groups

José Raposo (1997)

Studia Mathematica

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In [ABB] Asmar, Berkson and Bourgain prove that for a sequence ${ϕ_{j}}_{j = 1}^{\infty}$ of weak type (1, 1) multipliers in $ℝ^{n}$ and a function $k \in L^{1} (ℝ^{n})$ the weak type (1,1) constant of the maximal operator associated with ${k ⁎ ϕ_{j}}_{j}$ is controlled by that of the maximal operator associated with ${ϕ_{j}}_{j}$ . In [ABG] this theorem is extended to LCA groups with an extra hypothesis: the multipliers must be continuous. In this paper we prove a more general version of this last result without assuming the continuity of the multipliers. The proof...

The space Weak H¹

Robert Fefferman, Fernando Soria (1987)

Studia Mathematica

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Maximal seminorms on Weak $L^{1}$

Michael Cwikel, Charles Fefferman (1981)

Studia Mathematica

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Some weighted inequalities for general one-sided maximal operators

F. Martín-Reyes, A. de la Torre (1997)

Studia Mathematica

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We characterize the pairs of weights on ℝ for which the operators $M_{h, k}^{+} f (x) = s u p_{c > x} h (x, c) ʃ_{x}^{c} f (s) k (x, s, c) d s$ are of weak type (p,q), or of restricted weak type (p,q), 1 ≤ p < q < ∞, between the Lebesgue spaces with the coresponding weights. The functions h and k are positive, h is defined on $(x, c) : x < c$ , while k is defined on $(x, s, c) : x < s < c$ . If $h (x, c) = {(c - x)}^{- β}$ , $k (x, s, c) = {(c - s)}^{α - 1}$ , 0 ≤ β ≤ α ≤ 1, we obtain the operator $M_{α, β}^{+} f = s u p_{c > x} 1 / {(c - x)}^{β} ʃ_{x}^{c} f (s) / {(c - s)}^{1 - α} d s$ . For this operator, under the assumption 1/p - 1/q = α - β, we extend the weak type characterization to the case p = q and prove that in the case of equal...

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 $ℝ^{n}$ .

Variants of the Calderón-Zygmund theory for L-spaces.

Anthony Carbery (1986)

Revista Matemática Iberoamericana

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The purposes of this paper may be described as follows: (i) to provide a useful substitute for the Cotlar-Stein lemma for L^p-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions); (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea...

Weak-type multipliers

Peter Knopf (1980)

Studia Mathematica

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The dual of weak $L^{p}$

Michael Cwikel (1975)

Annales de l'institut Fourier

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For $1 < p < \infty$ , a characterization is given of the dual space of weak $L^{p}$ taken over a non atomic measure space.

A multiplier in Besov spaces which is not a multiplier in Lebesgue spaces

Hans Triebel (1979)

Banach Center Publications

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Isomorphism of certain weak $L^{p}$ spaces

Denny Leung (1993)

Studia Mathematica

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It is shown that the weak $L^{p}$ spaces $ℓ^{p, \infty}, L^{p, \infty} [0, 1]$ , and $L^{p, \infty} [0, \infty)$ are isomorphic as Banach spaces.

Displaying similar documents to “Restrictions from ℝ n to ℤ n of weak type (1,1) multipliers”

Displaying similar documents to “Restrictions from $ℝ^{n}$ to $ℤ^{n}$ of weak type (1,1) multipliers”