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Weighted norm inequalities for vector-valued singular integrals on homogeneous spaces

Sergio Antonio Tozoni (2004)

Studia Mathematica

Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis ( e j ) j ≥ 1 . Given an operator T from L c ∞ ( X ) to L¹(X), we consider the vector-valued extension T̃ of T given by T ̃ ( ∑ j f j e j ) = ∑ j T ( f j ) e j . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...

Weighted Orlicz space integral inequalities for the Hardy-Littlewood maximal operator

S. Bloom, R. Kerman (1994)

Studia Mathematica

Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies Δ 2 . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.

Weighted Sobolev-Lieb-Thirring inequalities.

Kazuya Tachizawa (2005)

Revista Matemática Iberoamericana

We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.

Weighted weak type inequalities for certain maximal functions

Hugo Aimar, Liliana Forzani (1991)

Studia Mathematica

We give an A_p type characterization for the pairs of weights (w,v) for which the maximal operator Mf(y) = sup 1/(b-a) ʃ_a^b |f(x)|dx, where the supremum is taken over all intervals [a,b] such that 0 ≤ a ≤ y ≤ b/ψ(b-a), is of weak type (p,p) with weights (w,v). Here ψ is a nonincreasing function such that ψ(0) = 1 and ψ(∞) = 0.

Weyl product algebras and classical modulation spaces

Anders Holst, Joachim Toft, Patrik Wahlberg (2010)

Banach Center Publications

We discuss continuity properties of the Weyl product when acting on classical modulation spaces. In particular, we prove that M p , q is an algebra under the Weyl product when p ∈ [1,∞] and 1 ≤ q ≤ min(p,p’).

What is a Sobolev space for the Laguerre function systems?

B. Bongioanni, J. L. Torrea (2009)

Studia Mathematica

We discuss the concept of Sobolev space associated to the Laguerre operator L α = - y d ² / d y ² - d / d y + y / 4 + α ² / 4 y , y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials ( L α ) - s . An appropriate Laguerre-Sobolev space is defined in order to achieve that coincidence. An application is given to the almost everywhere convergence of solutions of the Schrödinger equation. Other Laguerre operators are also considered.

What is van der Corput's lemma in higher dimensions?

Anthony Carbery, James Wright (2002)

Publicacions Matemàtiques

We consider variants of van der Corput's lemma in higher dimensions.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].

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