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The classical notion of Łojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of Łojasiewicz ideals in terms of properties of a generator. This characterization involves a certain type of estimates that differ from the usual Łojasiewicz inequality. We then show that basic properties of Łojasiewicz ideals in the $^{\infty}$ case have a Denjoy-Carleman counterpart.

[unknown]

G. Kyriazis (1998)

Studia Mathematica

We study smoothness spaces generated by maximal functions related to the local approximation errors of integral operators. It turns out that in certain cases these smoothness classes coincide with the spaces $C_{p}^{α} (ℝ^{d})$ , 0 < p≤∞, introduced by DeVore and Sharpley [DS] by means of the so-called sharp maximal functions of Calderón and Scott. As an application we characterize the $C_{p}^{α} (ℝ^{d})$ spaces in terms of the coefficients of wavelet decompositions.

αμ-duals and holomorphic (nuclear) mappings.

Manjul Gupta, P. K. Kamtham, G. M. Deheri (1985)

Collectanea Mathematica

τ-smooth linear functionals on vector lattices of real-valued functions

Wolfgang Adamski (1986)

Studia Mathematica

$ω$ –weighted holomorphic Besov spaces on the unit ball in $C^{n}$

A. V. Harutyunyan, Wolfgang Lusky (2011)

Commentationes Mathematicae Universitatis Carolinae

The $ω$ -weighted Besov spaces of holomorphic functions on the unit ball $B^{n}$ in $C^{n}$ are introduced as follows. Given a function $ω$ of regular variation and $0 < p < \infty$ , a function $f$ holomorphic in $B^{n}$ is said to belong to the Besov space $B_{p} (ω)$ if ${∥ f ∥}_{B_{p} (ω)}^{p} = \int_{B^{n}} {(1 - | z |}^{2})^{p} {| D f (z) |}^{p} \frac{ω (1 - | z |)}{{(1 - | z |}^{2})^{n + 1}} d ν (z) < + \infty,$ where $d ν (z)$ is the volume measure on $B^{n}$ and $D$ stands for the fractional derivative of $f$ . The holomorphic Besov space is described in the terms of the corresponding $L_{p} (ω)$ space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also,...

Алгебраические свойства сверток в $L_{2} (R_{N})$ .

В.Б. Коротков (1987)

Sibirskij matematiceskij zurnal

Алгебры, порожденные многомерными сингулярными интегральными операторами и коэффициентами, допускающими разрывы однородного типа

Н.Л. Василевский (1986)

Matematiceskij sbornik

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$𝒰 (ℱ)$ algebras and the symbolic calculus of Sebastião e Silva. (Les algèbres $𝒰 (ℱ)$ et le calcul symbolique de Sebastião e Silva.)

( $L_{p}$ , $L_{q}$ ) mapping properties of convolution transforms

$ℒ_{p}$ -Spaces and injective locally convex spaces [Book]

$(r, p)$ -absolutely summing operators on the space $C (T, X)$ and applications.

2-microlocal Besov and Triebel-Lizorkin spaces of variable integrability.

(Annexe) Convergence en mesure des séries aléatoires vectorielles à multiplicateur borné

(Conférence n°3) Applications radonifiantes dans l'espace des séries convergentes

(LB∞)-structure of spaces of germs of holomorphic functions.

Łojasiewicz ideals in Denjoy-Carleman classes

[unknown]

αμ-duals and holomorphic (nuclear) mappings.

τ-smooth linear functionals on vector lattices of real-valued functions

$ω$ –weighted holomorphic Besov spaces on the unit ball in $C^{n}$

Алгебраические свойства сверток в $L_{2} (R_{N})$ .

Алгебры, порожденные многомерными сингулярными интегральными операторами и коэффициентами, допускающими разрывы однородного типа

Аналоги неравенств Вейля и теоремы о следе в банаховом пространстве

Аналоги теоремы вложения Л.Карлесона для некоторых гильбертовых пространств аналитических функций

Анизoтропные соболевские классы в теории отображений

Аппроксимативные свойства подпространств конечной размерности в пространстве $L_{1}$

Аппроксимация потенциальных и соленоидальных векторных полей

Currently displaying 1 – 20 of 466

Displaying 1 – 20 of 466

ℒ p -Spaces and injective locally convex spaces [Book]

Currently displaying 1 – 20 of 466

$ℒ_{p}$ -Spaces and injective locally convex spaces [Book]