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• # Artykuł - szczegóły

## Studia Mathematica

2012 | 210 | 2 | 159-176

## Trace inequalities for fractional integrals in grand Lebesgue spaces

EN

### Abstrakty

EN
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.

159-176

wydano
2012

### Twórcy

• A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2, University St., 0186 Tbilisi, Georgia
autor
• A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2, University St., 0186 Tbilisi, Georgia
• Department of Mathematics, Faculty of Informatics and Control Systems, Georgian Technical University, 77, Kostava St., 0175 Tbilisi, Georgia