Convolution algebras with weighted rearrangement-invariant norm

Kerman, R.; Sawyer, E.

Kerman, R. ; Sawyer, E.

Studia Mathematica, Tome 108 (1994), p. 103-126 / Harvested from The Polish Digital Mathematics Library

Résumé

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).

Publié le : 1994-01-01

Zbl 0838.46020

EUDML-ID : urn:eudml:doc:216044

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     author = {R. Kerman and E. Sawyer},
     title = {Convolution algebras with weighted rearrangement-invariant norm},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {103-126},
     zbl = {0838.46020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv108i2p103bwm}
}

Kerman, R.; Sawyer, E. Convolution algebras with weighted rearrangement-invariant norm. Studia Mathematica, Tome 108 (1994) pp. 103-126. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv108i2p103bwm/

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