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

• Autorzy: Denise Szecsei
• Języki publikacji: EN

Abstrakty

EN

We define a class of measures having the following properties:
(1) the measures are supported on self-similar fractal subsets of the unit cube $I^{M} = [0,1)^{M}$, with 0 and 1 identified as necessary;
(2) the measures are singular with respect to normalized Lebesgue measure m on $I^{M}$;
(3) the measures have the convolution property that $μ∗ L^{p} ⊆ L^{p+ε}$ 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 $μ ∗ L^{p} ⊆ L^{q}$ for any measure μ in our class.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 43A05: Measures on groups and semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 109
• Numer: 2
• Strony: 171-177

Daty

wydano

2007

Twórcy

autor

Denise Szecsei

• Department of Mathematics, Stetson University, P.O. Box 7532, Daytona Beach, FL 32116, U.S.A.

Identyfikatory

DOI

10.4064/cm109-2-1