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Commutators with Coefficients in CMO of Weighted Hardy Operators in Generalized Local Morrey Spaces
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Number of Authors: 1
2017 (English)In: Mediterranean Journal of Mathematics, ISSN 1660-5446, E-ISSN 1660-5454, Vol. 14, no 2, 64Article in journal (Refereed) Published
Abstract [en]

We prove theorems on the boundedness of commutators [a,Hwα] of the weighted multidimensional Hardy operator Hwα:=wHα1w from a generalized local Morrey space Lp , φ ; 0(Rn) to local or global space Lq , ψ(Rn). The main impacts of these theorems are1.the use of CMOs-class of coefficients a for the commutators;2.the general setting when the function φ defining the Morrey space and the weight w are independent of one another and the weight w is not assumed to be in Ap;3.recovering the Sobolev–Adams exponent q instead of Sobolev–Spanne type exponent in the case of classical Morrey spaces4.boundedness from local to global Morrey spaces;5.the obtained estimates contain the parameter s> 1 which may be arbitrarily chosen. Its choice regulates in fact an equilibrium between assumptions on the coefficient a and the characteristics of the space. The obtained results are new also in non-weighted case

Place, publisher, year, edition, pages
2017. Vol. 14, no 2, 64
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-62481DOI: 10.1007/s00009-017-0872-3ISI: 000396095300030Scopus ID: 2-s2.0-85014458324OAI: oai:DiVA.org:ltu-62481DiVA: diva2:1081403
Note

Validerad; 2017; Nivå 2; 2017-03-14 (andbra)

Available from: 2017-03-14 Created: 2017-03-14 Last updated: 2017-11-24Bibliographically approved

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Samko, Natasha

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