All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 285

Showing per page

A convolution property of some measures with self-similar fractal support

Denise Szecsei (2007)

Colloquium Mathematicae

We define a class of measures having the following properties: (1) the measures are supported on self-similar fractal subsets of the unit cube , with 0 and 1 identified as necessary; (2) the measures are singular with respect to normalized Lebesgue measure m on ; (3) the measures have the convolution property that for some ε = ε(p) > 0 and all p ∈ (1,∞). We will show that if (1/p,1/q) lies in the triangle with vertices (0,0), (1,1) and (1/2,1/3), then for any measure μ in our class.

A convolution property of the Cantor-Lebesgue measure, II

Daniel M. Oberlin (2003)

Colloquium Mathematicae

For 1 ≤ p,q ≤ ∞, we prove that the convolution operator generated by the Cantor-Lebesgue measure on the circle is a contraction whenever it is bounded from to . We also give a condition on p which is necessary if this operator maps into L²().

A remark on the asymmetry of convolution operators

Saverio Giulini (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A convolution operator, bounded on L^{q}(\mathbb{R}^{n}), is bounded on L^{p}(\mathbb{R}^{n}), with the same operator norm, if p and q are conjugate exponents. It is well known that this fact is false if we replace \mathbb{R}^{n} with a general non-commutative locally compact group G. In this paper we give a simple construction of a convolution operator on a suitable compact group G, wich is bounded on L^{q}(G) for every q\in[2,\infty) and is unbounded on L^{p}(G) if p\in[1,2).

Currently displaying 1 – 20 of 285

Page 1 Next