Trace inequalities for fractional integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, and Alexander Meskhi. "Trace inequalities for fractional integrals in grand Lebesgue spaces." Studia Mathematica 210.2 (2012): 159-176. <http://eudml.org/doc/285396>.

@article{VakhtangKokilashvili2012,
abstract = {rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from $L^\{p),θ\}(X,μ)$ to $L^\{q),qθ/p\}(X,ν)$ (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.},
author = {Vakhtang Kokilashvili, Alexander Meskhi},
journal = {Studia Mathematica},
keywords = {grand Lebesgue spaces; potentials; fractional maximal functions; trace inequality; Fefferman-Stein inequality},
language = {eng},
number = {2},
pages = {159-176},
title = {Trace inequalities for fractional integrals in grand Lebesgue spaces},
url = {http://eudml.org/doc/285396},
volume = {210},
year = {2012},
}

TY - JOUR
AU - Vakhtang Kokilashvili
AU - Alexander Meskhi
TI - Trace inequalities for fractional integrals in grand Lebesgue spaces
JO - Studia Mathematica
PY - 2012
VL - 210
IS - 2
SP - 159
EP - 176
AB - rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from $L^{p),θ}(X,μ)$ to $L^{q),qθ/p}(X,ν)$ (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.
LA - eng
KW - grand Lebesgue spaces; potentials; fractional maximal functions; trace inequality; Fefferman-Stein inequality
UR - http://eudml.org/doc/285396
ER -