Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces
Joint Authors
Rahimova, Kamala R.
Guliyev, Vagif S.
Source
Journal of Function Spaces and Applications
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-12-24
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We prove that the parabolic fractional maximal operator MαP, 0≤α<γ, is bounded from the modified parabolic Morrey space M̃1,λ,P(ℝn) to the weak modified parabolic Morrey space WM̃q,λ,P(ℝn) if and only if α/γ≤1-1/q≤α/(γ-λ) and from M̃p,λ,P(ℝn) to M̃q,λ,P(ℝn) if and only if α/γ≤1/p-1/q≤α/(γ-λ).
Here γ=trP is the homogeneous dimension on ℝn.
In the limiting case (γ-λ)/α≤p≤γ/α we prove that the operator MαP is bounded from M̃p,λ,P(ℝn) to L∞(ℝn).
As an application, we prove the boundedness of MαP from the parabolic Besov-modified Morrey spaces BM̃pθ,λs(ℝn) to BM̃qθ,λs(ℝn).
As other applications, we establish the boundedness of some Schrödinger-ype operators on modified parabolic Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.
American Psychological Association (APA)
Guliyev, Vagif S.& Rahimova, Kamala R.. 2012. Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces. Journal of Function Spaces and Applications،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-480205
Modern Language Association (MLA)
Guliyev, Vagif S.& Rahimova, Kamala R.. Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces. Journal of Function Spaces and Applications No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-480205
American Medical Association (AMA)
Guliyev, Vagif S.& Rahimova, Kamala R.. Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces. Journal of Function Spaces and Applications. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-480205
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-480205