Mixed Morrey spaces

By T. Nogayama. Positivity (Dordrecht), 2018

104 citations recorded by the source corpus.

We introduce mixed Morrey spaces and show some basic properties. These properties extend the classical ones. We investigate the boundedness in these spaces of the iterated maximal operator, the fractional integral operator and singular integral operator. Furthermore, as a corollary, we obtain the boundedness of the iterated maximal operator in classical Morrey spaces. We also establish a version of the Fefferman–Stein vector-valued maximal inequality and some weighted inequalities for the iterated maximal operator in mixed Lebesgue spaces.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/837264bfc4bbb3c37e8ba7c980423a0c2644e08d

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Yangyang Zhang
4. Songbai Wang
5. Long Huang
6. Yoshihiro Sawano
7. Jun Liu
8. Ciqiang Zhuo

Citations in the corpus

• Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation (2019, background): “some other fields, the real-variable theory of mixed-norm function spaces, including mixed-norm Morrey spaces, mixed-norm Hardy spaces, mixed-norm Besov spaces and mixed-norm Triebel– Lizorkin spaces, has rapidly been developed in recent years (see, for instance, [20, 32, 63, 42, 43, 44]).”
• On Function Spaces with Mixed Norms — A Survey (2019, methodology): “To this end, we first recall the notion and some examples of mixed Morrey spaces Mp ~q (R n) from Nogayama [67] and then we further show some basic properties about these spaces, including the completeness as well as the embedding theorem, obtained in the same aforementioned article.”