Convolution algebras with weighted rearrangement-invariant norm
Studia Mathematica, Tome 108 (1994) no. 2, pp. 103-126
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $X(w) = {F: ℝ^n → ℂ: ∞ > ∥F∥_{X(w)} := ∥Fw∥_X}$. We investigate conditions on such a weight w that guarantee X(w) is an algebra under the convolution product F∗G defined at $x ∈ ℝ^n$ by $(F∗G)(x) = ʃ_{ℝ^n} F(x-y)G(y)dy$; more precisely, when $∥F∗G∥_{X(w)} ≤ ∥F∥_{X(w)} ∥G∥_{X(w)}$ for all F,G ∈ X(w).
@article{10_4064_sm_108_2_103_126,
author = {R. Kerman and E Sawyer},
title = {Convolution algebras with weighted rearrangement-invariant norm},
journal = {Studia Mathematica},
pages = {103--126},
publisher = {mathdoc},
volume = {108},
number = {2},
year = {1994},
doi = {10.4064/sm-108-2-103-126},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-108-2-103-126/}
}
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%0 Journal Article %A R. Kerman %A E Sawyer %T Convolution algebras with weighted rearrangement-invariant norm %J Studia Mathematica %D 1994 %P 103-126 %V 108 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm-108-2-103-126/ %R 10.4064/sm-108-2-103-126 %G en %F 10_4064_sm_108_2_103_126
R. Kerman; E Sawyer. Convolution algebras with weighted rearrangement-invariant norm. Studia Mathematica, Tome 108 (1994) no. 2, pp. 103-126. doi: 10.4064/sm-108-2-103-126
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