rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from to (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace inequalities for one-sided potentials, strong fractional maximal functions and potentials with product kernels, fractional maximal functions and potentials defined on the half-space are also proved in terms of Adams-type criteria. Finally, we remark that a Fefferman-Stein-type inequality for Hardy-Littlewood maximal functions and Calderón-Zygmund singular integrals holds in grand Lebesgue spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-2-4,
author = {Vakhtang Kokilashvili and Alexander Meskhi},
title = {Trace inequalities for fractional integrals in grand Lebesgue spaces},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {159-176},
zbl = {1275.46016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-2-4}
}
Vakhtang Kokilashvili; Alexander Meskhi. Trace inequalities for fractional integrals in grand Lebesgue spaces. Studia Mathematica, Tome 209 (2012) pp. 159-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-2-4/