The Fatou Property of Block Spaces

By Yoshihiro Sawano, Hitoshi Tanaka. 2014

102 citations recorded by the source corpus.

Around thirty years ago, block spaces, which are the predual of Morrey spaces, had been considered. However, it seems that there is no proof that block spaces satisfy the Fatou property. In this paper the Fatou property for block spaces is verified and the predual of block spaces is characterized.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d87db994cf09556dd317c9a040467b899d61ca58

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Yangyang Zhang
4. Yoshihiro Sawano
5. Songbai Wang
6. Xianjie Yan
7. Shohei Nakamura
8. Sibei Yang

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Yangyang Zhang
4. Songbai Wang
5. Yoshihiro Sawano
6. Shohei Nakamura
7. Xianjie Yan
8. Sibei Yang

Citations in the corpus

• Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces (2021, background): “Observe that the aforementioned several function spaces are not quasi-Banach function spaces (see, for instance, [64, 65, 74, 80]).”
• The singular integral operator and its commutator on weighted Morrey spaces (2016, background): “for all 0 < q < ∞ when w is a A∞ weight; for example [28], we have that ( 1 w(Q) ∫”
• Weak Hardy-type spaces associated with ball quasi-Banach function spaces I: Decompositions with applications to boundedness of Calderón-Zygmund operators (2019, background): “In recent decades, various variants of classical Hardy spaces have been introduced and their real-variable theories have been well developed; these variants include weighted Hardy spaces (see [64]), (weighted) Herz–Hardy spaces (see, for instance, [15, 26, 27, 52, 53]), (weighted) Hardy–Morrey space”
• Littlewood-Paley Characterizations of Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces (2019, background): “In recent decades, in order to meet the requirements arising in the study on the boundedness of operators, partial differential equations and some other analysis subjects, various variants of Hardy spaces have been introduced and their real-variable theories have been well developed; these variants ”
• Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation (2019, background): “In recent decades, various variants of classical Hardy spaces have been introduced and their real-variable theories have been well developed; these variants include weighted Hardy spaces (see [68]), (weighted) Herz–Hardy spaces (see, for instance, [18, 30, 31, 56, 57]), (weighted) Hardy–Morrey space”
• Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces (2020, background): “However, weighted Lebesgue spaces, Morrey spaces, mixed-norm Lebesgue spaces, Orlicz-slice spaces, and Musielak– Orlicz spaces are not necessarily quasi-Banach function spaces (see, for instance, [22,23,28,36] for more details and examples).”
• Banach function spaces done right (2023, background): “• Certain Morrey spaces do not satisfy (1.2), as was shown in [ST15, Example 3.3].”
• Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces (2019, background): “However, weighted Lebesgue spaces, Herz spaces, Morrey spaces and Musielak–Orlicz spaces are not necessarily quasi-Banach function spaces (see, for instance, [49, 55, 59] for more details and examples).”