Parabolic fractional maximal operator in modified parabolic Morrey spaces
type: Item
instance of: scholarly article
title: Parabolic fractional maximal operator in modified parabolic Morrey spaces
zbMATH Open document ID: 1259.42014
DOI: 10.1155/2012/543475
author: Vagif S. Guliyev
author: K. R. Rahimova
published in: Journal of Function Spaces and Applications
publication date: 2013-02-05T00:00:00Z
review text: Summary: We prove that the parabolic fractional maximal operator \(M^P_\alpha\), \(0 \leq \alpha < \gamma\), is bounded from the modified parabolic Morrey space \(\widetilde{M}_{1, \lambda, P}(\mathbb R^n)\) to the weak modified parabolic Morrey space \(W \widetilde{M}_{q, \lambda, P}(\mathbb R^n)\) if and only if \(\alpha/\gamma \leq 1 - 1/q \leq \alpha/(\gamma - \lambda)\) and from \(\widetilde{M}_{p, \lambda, P}(\mathbb R^n)\) to \(\widetilde{M}_{q, \lambda, P}(\mathbb R^n)\) if and only if \(\alpha/\gamma \leq 1/p - 1/q \leq \alpha/(\gamma - \lambda)\). Here \(\gamma = \operatorname{tr}P\) is the homogeneous dimension on \(\mathbb R^n\). In the limiting case \((\gamma - \lambda)/\alpha \leq p \leq \gamma/\alpha\), we prove that the operator \(M^P_\alpha\) is bounded from \(\widetilde{M}_{p, \lambda, P}(\mathbb R^n)\) to \(L_\infty(\mathbb R^n)\). As an application, we prove the boundedness of \(M^P_\alpha\) from the parabolic Besov-modified Morrey spaces \(\widetilde{BM}^s_{p\theta, \lambda}(\mathbb R^n)\) to \(\widetilde{BM}^s_{q\theta, \lambda} (\mathbb R^n)\). As another application, we establish the boundedness of some Schrödinger-type operators on modified parabolic Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 6134545
zbMATH Keywords: parabolic fractional operator
zbMATH Keywords: Morrey space
zbMATH Keywords: modified Morrey space
Wikidata QID: Q58908312
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/543475
OpenAlex ID: W2053103529
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description: scientific article; zbMATH DE number 6134545