Loading...
2 results
Search Results
Now showing 1 - 2 of 2
- Hardy type inequalityin variable lebesgue spacesPublication . Rafeiro, Humberto; Samko, StefanWe prove that in variable exponent spaces where L-p(.)(Omega), where p(.) satisfies the log-condition and Omega is a bounded domain in R-n with the property that R-n\(Omega) over bar has the cone property, the validity of the Hardy type inequality parallel to 1/delta(x)(alpha)integral(Omega)phi(y)/vertical bar x-y vertical bar(n-alpha)dy parallel to(p(.)) <= C parallel to phi parallel to(p(.)), 0 < alpha < min (1, n/p(+)), where delta(x) is approximately equal to dist(x, partial derivative Omega), is equivalent to a certain property of the domain Omega expressed in terms of alpha and chi(Omega).
- Inversion of the Bessel potential operator in weighted variable Lebesgue spacesPublication . Almeida, Alexandre; Rafeiro, HumbertoWe study the inversion problem of the Bessel potential operator within the frameworks of the weighted Lebesgue spaces with variable exponent. The inverse operator is constructed by using pproximative inverse operators. This generalizes some classical results to the variable exponent setting. (c) 2007 Elsevier Inc. All rights reserved.