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Best constants for some operators associated with the Fourier and Hilbert transforms

B. Hollenbeck, N. J. Kalton, I. E. Verbitsky (2003)

Studia Mathematica

We determine the norm in L p ( ℝ ₊ ) , 1 < p < ∞, of the operator I - ℱ s ℱ c , where ℱ c and ℱ s are respectively the cosine and sine Fourier transforms on the positive real axis, and I is the identity operator. This solves a problem posed in 1984 by M. S. Birman [Bir] which originated in scattering theory for unbounded obstacles in the plane. We also obtain the L p -norms of the operators aI + bH, where H is the Hilbert transform (conjugate function operator) on the circle or real line, for arbitrary real a,b. Best...

Biduality in (LF)-spaces.

Klaus D. Bierstedt, José Bonet (2001)

RACSAM

En la Sección 1 se pueban resultados abstractos sobre preduales y sobre bidualidad de espacios (LF). Sea E = indn En un espacio (LF), ponemos H = indn Hn para una sucesión de subespacios de Fréchet Hn de En con Hn ⊂ Hn+1. Investigamos bajo qué condiciones el espacio E es canónicamente (topológicamente isomorfo a) el bidual inductivo (H'b)'i o (incluso) al bidual fuerte de H. Los resultados abstractos se aplican en la Sección 2, especialmente a espacios (LF) ponderados de funciones holomorfas, pero...

Binomial-Poisson entropic inequalities and the M/M/∞ queue

Djalil Chafaï (2006)

ESAIM: Probability and Statistics

This article provides entropic inequalities for binomial-Poisson distributions, derived from the two point space. They appear as local inequalities of the M/M/∞ queue. They describe in particular the exponential dissipation of Φ-entropies along this process. This simple queueing process appears as a model of “constant curvature”, and plays for the simple Poisson process the role played by the Ornstein-Uhlenbeck process for Brownian Motion. Some of the inequalities are recovered by semi-group ...

Biseparating maps on generalized Lipschitz spaces

Denny H. Leung (2010)

Studia Mathematica

Let X, Y be complete metric spaces and E, F be Banach spaces. A bijective linear operator from a space of E-valued functions on X to a space of F-valued functions on Y is said to be biseparating if f and g are disjoint if and only if Tf and Tg are disjoint. We introduce the class of generalized Lipschitz spaces, which includes as special cases the classes of Lipschitz, little Lipschitz and uniformly continuous functions. Linear biseparating maps between generalized Lipschitz spaces are characterized...

Bloch type spaces on the unit ball of a Hilbert space

Zhenghua Xu (2019)

Czechoslovak Mathematical Journal

We initiate the study of Bloch type spaces on the unit ball of a Hilbert space. As applications, the Hardy-Littlewood theorem in infinite-dimensional Hilbert spaces and characterizations of some holomorphic function spaces related to the Bloch type space are presented.

BMO and Lipschitz approximation by solutions of elliptic equations

Joan Mateu, Yuri Netrusov, Joan Orobitg, Joan Verdera (1996)

Annales de l'institut Fourier

We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak * spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.

BMO-scale of distribution on ℝ n

René Erlín Castillo, Julio C. Ramos Fernández (2008)

Czechoslovak Mathematical Journal

Let S ' be the class of tempered distributions. For f ∈ S ' we denote by J - α f the Bessel potential of f of order α . We prove that if J - α f ∈ B M O , then for any λ ∈ ( 0 , 1 ) , J - α ( f ) λ ∈ B M O , where ( f ) λ = λ - n f ( φ ( λ - 1 · ) ) , φ ∈ S . Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order α > 0 belongs to the V M O space.

Currently displaying 61 – 80 of 125