Geodesic
Convolution algebras with weighted rearrangement-invariant norm
Studia Mathematica, Tome 108 (1994) no. 2, pp. 103-126 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $X(w) = {F: ℝ^n → ℂ: ∞ > ∥F∥_{X(w)} := ∥Fw∥_X}$. 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). 
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     author = {R. Kerman and E Sawyer},
     title = {Convolution algebras with weighted rearrangement-invariant norm},
     journal = {Studia Mathematica},
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     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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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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