Necessary and sufficient conditions for the boundedness of fractional maximal operators in local Morrey-type spaces

By Victor Burenkov, H. Guliyev, Vagif S. Guliyev. 2007

95 citations recorded by the source corpus.

The problem of the boundedness of the fractional maximal operator Mα, 0 < α < n, in local and global Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters. Moreover, in case of local Morrey-type spaces, for some values of the parameters, these sufficient conditions coincide with the necessary ones.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e455b8cf8a71429a4ce9639229558accc3e88cd0

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In Applied Mathematics

1. Vagif S. Guliyev
2. R. Mustafayev
3. Amiran Gogatishvili
4. Victor Burenkov
5. Yoshihiro Sawano
6. A. Meskhi
7. S. Samko

In Mathematical Physics

1. Vagif S. Guliyev
2. R. Mustafayev
3. Amiran Gogatishvili
4. Victor Burenkov
5. Yoshihiro Sawano
6. A. Meskhi

Citations in the corpus

• Weighted Hardy and potential operators in the generalized Morrey spaces (2011, unknown): “Obviously, L (Ω) ⊂ L p,φ loc;x0 The spaces L p,φ(Ω), L p,φ loc;x0 (Ω) are known under the names of global and local Morrey spaces, see for instance [7,8].”
• Boundedness of the fractional maximal operator in local Morrey-type spaces (2010, methodology): “In [5]-[ 8 ] the boundedness of maximal and fractional maximal operators from”