English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove theorems on the boundedness of commutators $$[a,H_w^\alpha ]$$[a,Hwα] of the weighted multidimensional Hardy operator $$H^\alpha _w:= w H^\alpha \frac{1}{w}$$Hwα:=wHα1w from a generalized local Morrey space $$\mathcal {L}^{p,\varphi ;0}({\mathbb {R}^n})$$Lp,φ;0(Rn) to local or global space $$\mathcal {L}^{q,\psi }({\mathbb {R}^n})$$Lq,ψ(Rn). The main impacts of these theorems are1.the use of CMO$$_s$$s-class of coefficients a for the commutators;2.the general setting when the function $$\varphi $$φ defining the Morrey space and the weight w are independent of one another and the weight w is not assumed to be in $$A_p$$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 $$s > 1$$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.

Commutators with Coefficients in CMO of Weighted Hardy Operators in Generalized Local Morrey Spaces