Displaying similar documents to “Pointwise estimates for densities of stable semigroups of measures”

The convolution equation P = P * Q of Choquet and Deny and relatively invariant measures on semigroups

Arunava Mukherjea (1971)

Annales de l'institut Fourier

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Choquet and Deny considered on an abelian locally compact topological group the representation of a measure P as the convolution product of itself and a finite measure Q : P = P * Q . In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions P of the above equation which are relatively invariant on the support of Q . A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results...

On maximal functions over circular sectors with rotation invariant measures

Hugo A. Aimar, Liliana Forzani, Virginia Naibo (2001)

Commentationes Mathematicae Universitatis Carolinae

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Given a rotation invariant measure in ℝ n , we define the maximal operator over circular sectors. We prove that it is of strong type ( p , p ) for p > 1 and we give necessary and sufficient conditions on the measure for the weak type ( 1 , 1 ) inequality. Actually we work in a more general setting containing the above and other situations.

On the maximal function for rotation invariant measures in ℝ n

Ana Vargas (1994)

Studia Mathematica

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Given a positive measure μ in ℝ n , there is a natural variant of the noncentered Hardy-Littlewood maximal operator M μ f ( x ) = s u p x ∈ B 1 / μ ( B ) ʃ B | f | d μ , where the supremum is taken over all balls containing the point x. In this paper we restrict our attention to rotation invariant, strictly positive measures μ in ℝ n . We give some necessary and sufficient conditions for M μ to be bounded from L 1 ( d μ ) to L 1 , ∞ ( d μ ) .

On the weak L 1 space and singular measures

Robert Kaufman (1982)

Annales de l'institut Fourier

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We study the class of singular measures whose Fourier partial sums converge to 0 in the metric of the weak L 1 space; symmetric sets of constant ratio occur in an unexpected way.