Displaying similar documents to “Good weights for weighted convolution algebras”

Weak* properties of weighted convolution algebras II

Sandy Grabiner (2010)

Studia Mathematica

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We show that if ϕ is a continuous homomorphism between weighted convolution algebras on ℝ⁺, then its extension to the corresponding measure algebras is always weak* continuous. A key step in the proof is showing that our earlier result that normalized powers of functions in a convolution algebra on ℝ⁺ go to zero weak* is also true for most measures in the corresponding measure algebra. For some algebras, we can determine precisely which measures have normalized powers converging to zero...

General Gagliardo Inequality and Applications to Weighted Sobolev Spaces

Antonio Avantaggiati, Paola Loreti (2009)

Bollettino dell'Unione Matematica Italiana

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In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].

Rademacher functions in weighted Cesàro spaces

Javier Carrillo-Alanís (2013)

Studia Mathematica

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We study the behaviour of the Rademacher functions in the weighted Cesàro spaces Ces(ω,p), for ω(x) a weight and 1 ≤ p ≤ ∞. In particular, the case when the Rademacher functions generate in Ces(ω,p) a closed linear subspace isomorphic to ℓ² is considered.

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 n , such as the classical Lebesgue, Lorentz or Orlicz spaces. Given a nonnegative, measurable (weight) function on n , define X ( w ) = F : n : > 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 n by ( F G ) ( x ) = ʃ n F ( x - y ) G ( y ) d y ; more precisely, when F G X ( w ) F X ( w ) G X ( w ) for all F,G ∈ X(w).

Weighted composition operators on weighted Lorentz spaces

İlker Eryilmaz (2012)

Colloquium Mathematicae

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The boundedness, compactness and closedness of the range of weighted composition operators acting on weighted Lorentz spaces L(p,q,wdμ) for 1 < p ≤ ∞, 1 ≤ q ≤ ∞ are characterized.