Molecular decomposition of anisotropic homogeneous mixed-norm spaces with applications to the boundedness of operators

By G. Cleanthous, Athanasios G. Georgiadis, Morten Nielsen. Applied and Computational Harmonic Analysis, 2017

78 citations recorded by the source corpus.

Abstract Anisotropic homogeneous mixed-norm Besov and Triebel–Lizorkin spaces are introduced and their properties are explored. A discrete adapted φ -transform decomposition is obtained. An associated class of almost diagonal operators is introduced and a boundedness result for such operators is obtained. Molecular decompositions for all the considered spaces are derived with the help of the algebra of almost diagonal operators. As an application, we obtain boundedness results on the considered spaces for Fourier multipliers and for pseudodifferential operators with suitable adapted homogeneous symbols using the molecular decomposition theory.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/47b9df21c0842ece24b0980b2b083c071b9ec132

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In Applied Mathematics

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

Citations in the corpus

• On Function Spaces with Mixed Norms — A Survey (2019, background): “For more progresses about various function spaces with mixed norms and their applications in the boundedness of different operators, we refer the reader to [18, 20, 22, 33, 34, 38, 39, 47–50].”
• Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, background): “Moreover, very recently, there appears a renewed increasing interest in the theory of mixed-norm function spaces, including mixed-norm Lebesgue spaces, mixed-norm Hardy spaces, mixed-norm Besov spaces and mixed-norm Triebel-Lizorkin spaces; see, for example, [19, 20, 30, 38, 39, 40, 41].”
• Dual spaces of anisotropic mixed-norm Hardy spaces (2018, background): “In addition, the theory of anisotropic or mixed-norm function spaces was developed well in recent years; see, for example, [6, 7, 9, 14, 18].”