Processing math: 100%

Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves

Citation:
Karlovich, Alexei Yu. "Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves." Mathematische Nachrichten. 283 (2010): 85-93.

Abstract:

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights φt,γ(τ)=|(τt)γ|, where γ is a complex number, over arbitrary Carleson curves. If the curve has different spirality indices at the point $t$ and γ is not real, then φt,γ is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko.

Related External Link

Preprint in arXiv:

http://arxiv.org/abs/0808.0258

loading