Hardy type inequality in variable Lebesgue spaces

Details Hardy type inequality in variable Lebesgue spaces Hardy type inequality in variable Lebesgue spaces

2008-04-22

arxiv.org/abs/0804.3511v4

Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 1, 279--289

Mathematics

Functional Analysis

16 pages

Scientific paper

We prove that in variable exponent spaces $L^{p(\cdot)}(\Omega)$, where $p(\cdot)$ satisfies the log-condition and $\Omega$ is a bounded domain in $\mathbf R^n$ with the property that $\mathbf R^n \backslash \bar{\Omega}$ has the cone property, the validity of the Hardy type inequality $$| 1/\delta(x)^\alpha \int_\Omega \phi(y) dy/|x-y|^{n-\alpha}|_{p(\cdot)} \leqq C |\phi|_{p(\cdot)}, \quad 0<\al<\min(1,\frac{n}{p_+})$$, where $\delta(x)=\mathrm{dist}(x,\partial\Omega)$, is equivalent to a certain property of the domain $\Om$ expressed in terms of $\al$ and $\chi_\Om$.

Affiliated with

Also associated with

No associations

Rating

Hardy type inequality in variable Lebesgue spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hardy type inequality in variable Lebesgue spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hardy type inequality in variable Lebesgue spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-675474