Trace inequalities for fractional integrals in grand Lebesgue spaces

• Autorzy: Vakhtang Kokilashvili , Alexander Meskhi
• Języki publikacji: 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.

Kategorie tematyczne

• 31E05: Potential theory on metric spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 210
• Numer: 2
• Strony: 159-176

Daty

wydano

2012

Twórcy

autor

Vakhtang Kokilashvili

• A. Razmadze Mathematical Institute, I. Javakhishvili Tbilisi State University, 2, University St., 0186 Tbilisi, Georgia

autor

Alexander Meskhi

• 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

Identyfikatory

DOI

10.4064/sm210-2-4