A note on $L_p$-algebras

Wiesław Żelazko

Displaying similar documents to “A note on $L_{p}$ -algebras”

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...

On the algebras $L_{p}$ of locally compact groups

Wiesław Żelazko (1961)

Colloquium Mathematicae

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Convolutions and factorization theorems

R. Rao Chivukula, Randall K. Heckman (1974)

Compositio Mathematica

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Convolution algebras with weighted rearrangement-invariant norm

R. Kerman, E. Sawyer (1994)

Studia Mathematica

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Let X be a rearrangement-invariant space of Lebesgue-measurable functions on $ℝ^{n}$ , such as the classical Lebesgue, Lorentz or Orlicz spaces. Given a nonnegative, measurable (weight) function on $ℝ^{n}$ , define $X (w) = F : ℝ^{n} \to ℂ : \infty > ∥ F ∥_{X (w)} : = ∥ F w ∥_{X}$ . We investigate conditions on such a weight w that guarantee X(w) is an algebra under the convolution product F∗G defined at $x \in ℝ^{n}$ by $(F * G) (x) = ʃ_{ℝ^{n}} F (x - y) G (y) d y$ ; more precisely, when $∥ F * G ∥_{X (w)} \leq ∥ F ∥_{X (w)} ∥ G ∥_{X (w)}$ for all F,G ∈ X(w).