Weighted Hardy and potential operators in the generalized Morrey spaces
By Lars-Erik Persson, Natasha Samko. 2011
63 citations recorded by the source corpus.
Abstract We study the weighted p → q -boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces L p , φ ( R n , w ) defined by an almost increasing function φ ( r ) and radial type weight w ( | x | ) . We obtain sufficient conditions, in terms of some integral inequalities imposed on φ and w , for such a p → q -boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p → q -boundedness of the Riesz potential operator.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6d4a2ac86d060e4ae583f602825b905aceb693f0
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In Applied Mathematics
- Yoshihiro Sawano
- Peter Wall
- M. Alessandra Ragusa
- Lars-Erik Persson
- Natasha Samko
- Shohei Nakamura
- Dachun Yang
- S. Samko
In Mathematical Physics
- Yoshihiro Sawano
- M. Alessandra Ragusa
- Peter Wall
- Natasha Samko
- Lars-Erik Persson
- Dachun Yang
- Wen Yuan
- S. Samko
Citations in the corpus
- Commutators of Hardy operators in vanishing Morrey spaces (2012, methodology): “2 in [19], but it holds for anyΠ, since the proof in [19] was beside on the pointwise estimate via the norm of a function in L loc,0, see the inequality (4.”
- Weighted Hardy operators in the local generalized vanishing Morrey spaces (2012, unknown): “We follow the main ideas of the proof in [23] and have ∫ |z|<r | f (z)|s v (|z|) dz = ∞ ∑ k=0 ∫”
- A Thought on Generalized Morrey Spaces (2018, background): “See [3, 12, 89, 91, 92, 112] for another notation of generalized Morrey spaces, for example.”