Abstract
We introduce weighted generalized Grand Morrey spaces and prove that the boundedness of linear operators from the generalized Grand Lebesgue spaces to generalized Morrey spaces may be derived from their boundedness from classical weighted Lebesgue spaces into weighted Morrey spaces. As an application we prove a theorem on mapping properties of the Riesz potential operator from weighted generalized Grand Lebesgue spaces to weighted generalized Grand Morrey spaces with Muckenhoupt–Wheeden A p,q-weights, under some natural assumptions on the way how we generalize grand spaces.
Mathematics Subject Classification (2010). Primary 46E15; Secondary 42B35.
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Umarkhadzhiev, S. (2014). The Boundedness of the Riesz Potential Operator from Generalized Grand Lebesgue Spaces to Generalized Grand Morrey Spaces. In: Bastos, M., Lebre, A., Samko, S., Spitkovsky, I. (eds) Operator Theory, Operator Algebras and Applications. Operator Theory: Advances and Applications, vol 242. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0816-3_22
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DOI: https://doi.org/10.1007/978-3-0348-0816-3_22
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