Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces
Joint Authors
Rahimova, Kamala R.
Guliyev, Vagif S.
Source
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،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-994235
Modern Language Association (MLA)
Guliyev, Vagif S.& Rahimova, Kamala R.. Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces. Journal of Function Spaces No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-994235
American Medical Association (AMA)
Guliyev, Vagif S.& Rahimova, Kamala R.. Parabolic Fractional Maximal Operator in Modified Parabolic Morrey Spaces. Journal of Function Spaces. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-994235
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-994235