Convolution algebras with weighted rearrangement-invariant norm

R. Kerman; E. Sawyer

Displaying similar documents to “Convolution algebras with weighted rearrangement-invariant norm”

On a class of convolution algebras of functions

Hans G. Feichtinger (1977)

Annales de l'institut Fourier

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The Banach spaces $Λ (A, B, X, G)$ defined in this paper consist essentially of those elements of $L^{1} (G)$ ( $G$ being a locally compact group) which can in a certain sense be well approximated by functions with compact support. The main result of this paper is the fact that in many cases $Λ (A, B, X, G)$ becomes a Banach convolution algebra. There exist many natural examples. Furthermore some theorems concerning inclusion results and the structure of these spaces are given. In particular we prove that simple conditions imply...

Convolution of functions in Lorentz spaces

Leonard Yap (1971)

Studia Mathematica

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A note on $L_{p}$ -algebras

Wiesław Żelazko (1963)

Colloquium Mathematicae

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The class of convolution operators on the Marcinkiewicz spaces

Ka-Sing Lau (1981)

Annales de l'institut Fourier

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Let $𝒯_{X}$ denote the operator-norm closure of the class of convolution operators $Φ_{μ} : X \to X$ where $X$ is a suitable function space on $R$ . Let $ℳ_{r}^{p}$ be the closed subspace of regular functions in the Marinkiewicz space $ℳ^{p}$ , $1 \leq p < \infty$ . We show that the space $𝒯_{ℳ_{r}^{p}}$ is isometrically isomorphic to $𝒯_{L^{p}}$ and that strong operator sequential convergence and norm convergence in $𝒯_{ℳ_{r}^{p}}$ coincide. We also obtain some results concerning convolution operators under the Wiener transformation. These are to improve a Tauberian theorem of Wiener...

A convolution approximation property for $L^{1}$ (G)

Louis Pigno (1976)

Studia Mathematica

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A theorem on the discrete groups and algebras $L_{p}$

Wiesław Żelazko (1961)

Colloquium Mathematicae

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On decompositions in generalised Lorentz-Zygmund spaces

J. S. Neves (2001)

Bollettino dell'Unione Matematica Italiana

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Il lavoro presenta diverse caratterizzazioni degli spazi Lorentz-Zygmund generalizzati (GLZ) $L_{p, q; α} (R)$ , con $p, q \in (0, + \infty]$ , $m \in N$ , $α \in R^{m}$ e $(R, μ)$ spazio misurato con misura $μ (R)$ finita. Dato uno spazio misurato $(R, μ)$ e $α \in R_{-}^{m}$ , otteniamo representazioni equivalenti per la (quasi-) norma dello spazio GLZ $L_{\infty, \infty; α} (R)$ . Inoltre, se $(R, μ)$ è uno spazio misurato con misura finita e $α \in R_{+}^{m}$ , viene presentata in termini di decomposizioni una norma equivalente per lo spazio $L_{1, 1; α} (R)$ . Si dimostra che le norme equivalenti considerate per $L_{\infty, \infty; α} (R)$ , con $(R, μ)$ uno spazio a misura...

Weighted convolution algebras on subsemigroups of the real line

H. G. Dales, H. V. Dedania

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In this memoir, we shall consider weighted convolution algebras on discrete groups and semigroups, concentrating on the group (ℚ,+) of rational numbers, the semigroup $(ℚ^{+ •}, +)$ of strictly positive rational numbers, and analogous semigroups in the real line ℝ. In particular, we shall discuss when these algebras are Arens regular, when they are strongly Arens irregular, and when they are neither, giving a variety of examples. We introduce the notion of ’weakly diagonally bounded’ weights, weakening...

Compact convolution operators between $L_{p} (G)$ -spaces

G. Crombez, W. Govaerts (1978)

Colloquium Mathematicae

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