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Displaying 101 – 120 of 1406

A₁-regularity and boundedness of Calderón-Zygmund operators

Dmitry V. Rutsky (2014)

Studia Mathematica

The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and...

Abelian ergodic theorems for contraction semigroups

S. McGrath (1977)

Studia Mathematica

About interpolation of subspaces of rearrangement invariant spaces generated by Rademacher system.

Astashkin, Sergey V. (2001)

International Journal of Mathematics and Mathematical Sciences

Abstract characterization of Orlicz-Kantorovich lattices associated with an $L_{0}$ -valued measure

Botir Zakirov (2008)

Commentationes Mathematicae Universitatis Carolinae

An abstract characterization of Orlicz-Kantorovich lattices constructed by a measure with values in the ring of measurable functions is presented.

Abstract Korovkin-type theorems in modular spaces and applications

Carlo Bardaro, Antonio Boccuto, Xenofon Dimitriou, Ilaria Mantellini (2013)

Open Mathematics

We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the...

Addendum to: "Linear operations, tensor products, and contractive projections in function spaces" (Studia Math. 38 (1970), pp. 131-186)

M. Rao (1973)

Studia Mathematica

Addendum to "Necessary condition for Kostyuchenko type systems to be a basis in Lebesgue spaces" (Colloq. Math. 127 (2012), 105-109)

Aydin Sh. Shukurov (2014)

Colloquium Mathematicae

It is well known that if φ(t) ≡ t, then the system ${φ ⁿ (t)}_{n = 0}^{\infty}$ is not a Schauder basis in L₂[0,1]. It is natural to ask whether there is a function φ for which the power system ${φ ⁿ (t)}_{n = 0}^{\infty}$ is a basis in some Lebesgue space $L_{p}$ . The aim of this short note is to show that the answer to this question is negative.

Addendum to "On Some Space of Vector Valued Sequences".

Nguyen Phuong-Cac (1971)

Mathematische Zeitschrift

Adhérence faible étoile d'algèbres de fractions rationnelles

Jacques Chaumat (1974)

Annales de l'institut Fourier

Étant donnés un compact $K$ du plan complexe, et une mesure non nulle sur $K$ , on étudie $H^{\infty} (μ)$ , l’adhérence dans $L^{\infty} (μ)$ , pour la topologie $σ (L^{\infty} (μ), L^{1} (μ))$ , de l’algèbre des fractions rationnelles d’une variable complexe, à pôles hors de $K$ . Le résultat principal obtenu est qu’il existe un sous-ensemble $E_{μ}$ de $K$ , éventuellement vide, mesurable pour la mesure de Lebesgue plane, et une mesure $μ_{s}$ , éventuellement nulle, absolument continue par rapport à la mesure $μ$ , tels que : $H^{\infty} (μ)$ soit isométriquement isomorphe à $H^{\infty} (λ_{E_{μ}}) \oplus L^{\infty} (μ_{s})$ , où $λ_{E_{μ}}$ désigne la...

Admissible and regular potentials for positive Co-semigroups and application to heat semigroups.

M. Ishikawa (1994)

Semigroup forum

Algebraic genericity of strict-order integrability

Luis Bernal-González (2010)

Studia Mathematica

We provide sharp conditions on a measure μ defined on a measurable space X guaranteeing that the family of functions in the Lebesgue space $L^{p} (μ, X)$ (p ≥ 1) which are not q-integrable for any q > p (or any q < p) contains large subspaces of $L^{p} (μ, X)$ (without zero). This improves recent results due to Aron, García, Muñoz, Palmberg, Pérez, Puglisi and Seoane. It is also shown that many non-q-integrable functions can even be obtained on any nonempty open subset of X, assuming that X is a topological space and...

Algebras of singular integral operators on rearrangement-invariant spaces and Nikolski ideals.

Karlovich, Alexei Yu. (2002)

The New York Journal of Mathematics [electronic only]

Algèbres de fonctions à orthogonal purement atomique

L. Chevalier (1971)

Studia Mathematica

Algèbres $L^{1}$ $p$ -adiques

Jean Fresnel, Bernard De Mathan (1978)

Bulletin de la Société Mathématique de France

Almost regular operators and integral operators on rearrangement invariant p-spaces of functions, $0 < p < = 1$

Popa, Nicolae (1984)

Proceedings of the 12th Winter School on Abstract Analysis

Almost sure approximation of unbounded operators in $L_{2} (X, A, μ)$

Ryszard Jajte, Adam Paszkiewicz (1998)

Studia Mathematica

The possibilities of almost sure approximation of unbounded operators in $L_{2} (X, A, μ)$ by multiples of projections or unitary operators are examined.

Alternative characterisations of Lorentz-Karamata spaces

David Eric Edmunds, Bohumír Opic (2008)

Czechoslovak Mathematical Journal

We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.

An application of a theorem of Hirsberg and Lazar.

Asvald Lima (1976)

Mathematica Scandinavica

An atomic decomposition of the predual of BMO(ρ).

Beatriz E. Viviani (1987)

Revista Matemática Iberoamericana

We study the Orlicz type spaces Hω, defined as a generalization of the Hardy spaces Hp for p ≤ 1. We obtain an atomic decomposition of Hω, which is used to provide another proof of the known fact that BMO(ρ) is the dual space of Hω (see S. Janson, 1980, [J]).

An elementary approach to some questions in higher order smoothness in Banach spaces.

M. Fabián, V. Zizler (1999)

Extracta Mathematicae

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