Displaying similar documents to “Subalgebras to a Wiener type algebra of pseudo-differential operators”

Fefferman's SAK principle in one dimension

Frédéric Hérau (2000)

Annales de l'institut Fourier

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In this article we give a complete proof in one dimension of an a priori inequality involving pseudo-differential operators: if a and b are symbols in S 1 , 0 2 such that | a | ≤ b , then for all ϵ > 0 we have the estimate ∥ a w u ∥ s 2 ≤ C ϵ ( ∥ b w u ∥ s 2 + ∥ u ∥ s + ϵ 2 ) for all u in the Schwartz space, where ∥ ∥ t is the usual H t norm. We use microlocalization of levels I, II and III in the spirit of Fefferman’s SAK principle.

Iterates and the boundary behavior of the Berezin transform

Jonathan Arazy, Miroslav Engliš (2001)

Annales de l’institut Fourier

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Let μ be a measure on a domain Ω in ℂ n such that the Bergman space of holomorphic functions in L 2 ( Ω , μ ) possesses a reproducing kernel K ( x , y ) and K ( x , x ) > 0 ∀ x ∈ Ω . The Berezin transform associated to μ is the integral operator B f ( y ) = K ( y , y ) - 1 ∫ Ω f ( x ) | K ( x , y ) | 2 d μ ( x ) . The number B f ( y ) can be interpreted as a certain mean value of f around y , and functions satisfying B f = f as functions having a certain mean-value property. In this paper we investigate the boundary behavior of B f , the existence of functions f satisfying...

On functions whose translates are independent

Ralph E. Edwards (1951)

Annales de l'institut Fourier

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Ce travail est l’étude de divers cas particuliers d’un problème nouveau, semble-t-il, concernant les translatées de fonctions ou de distributions sur un groupe. Soit E un espace vectoriel topologique de fonctions ou de distributions sur un groupe abélien G localement compact ; E est supposé invariant par les translations a → f a ( x ) = f ( x + a ) ( f ∈ E , a ∈ G ) . Si f ∈ E et si A est un sous-ensemble non vide de G , I ( f , A ) = I ( f , A , E ) désigne le sous-espace vectoriel fermé de E engendré par les translatées f a de f avec a ∈ A . On dira qu’une f ∈ E a ses...

L p - L q estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Michael Cowling, Saverio Giulini, Stefano Meda (2001)

Annales de l’institut Fourier

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Let X be a symmetric space of the noncompact type, with Laplace–Beltrami operator - ℒ , and let [ b , ∞ ) be the L 2 ( X ) -spectrum of ℒ . For τ in ℂ such that Re τ ≥ 0 , let 𝒫 τ be the operator on L 2 ( X ) defined formally as exp ( - τ ( ℒ - b ) 1 / 2 ) . In this paper, we obtain L p - L q operator norm estimates for 𝒫 τ for all τ , and show that these are optimal when τ is small and when | arg τ | is bounded below π / 2 .

Uncertainty principles for integral operators

Saifallah Ghobber, Philippe Jaming (2014)

Studia Mathematica

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The aim of this paper is to prove new uncertainty principles for integral operators with bounded kernel for which there is a Plancherel Theorem. The first of these results is an extension of Faris’s local uncertainty principle which states that if a nonzero function f ∈ L ² ( ℝ d , μ ) is highly localized near a single point then (f) cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function f ∈ L ² ( ℝ d , μ ) and...

Absolute convergence of multiple Fourier integrals

Yurii Kolomoitsev, Elijah Liflyand (2013)

Studia Mathematica

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Various new sufficient conditions for representation of a function of several variables as an absolutely convergent Fourier integral are obtained. The results are given in terms of L p integrability of the function and its partial derivatives, each with a different p. These p are subject to certain relations known earlier only for some particular cases. Sharpness and applications of the results obtained are also discussed.