, Volume 17, Issue 3, pp 683–706

Weighted Hardy operators in the local generalized vanishing Morrey spaces


DOI: 10.1007/s11117-012-0199-z

Cite this article as:
Samko, N. Positivity (2013) 17: 683. doi:10.1007/s11117-012-0199-z


In this paper we study \(p\rightarrow q\)-boundedness of the multi-dimensional Hardy type operators in the vanishing local generalized Morrey spaces \(V\mathcal L ^{p,\varphi }_\mathrm{{loc}}(\mathbb R ^n,w)\) defined by an almost increasing function \(\varphi (r)\) and radial type weight \(w(|x|)\). We obtain sufficient conditions, in terms of some integral inequalities imposed on \(\varphi \) and \(w\), for such a boundedness. In the case where the function \(\varphi (r)\) and the weight are power functions, these conditions are also necessary.


Generalized weighted Morrey spaceLocal Morrey spaces Weighted Hardy inequalitiesWeighted Hardy operatorsBary-Stechkin classesMatuszewska-Orlicz indices

Mathematics Subject Classification (2000)


Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Departamento de Matematica, Centro CEAFInstituto Superior TécnicoLisboaPortugal
  2. 2.Luleå University of TechnologyLuleåSweden