Hardy spaces with variable exponents and generalized Campanato spaces

By E. Nakai, Yoshihiro Sawano. 2012

419 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2619de5c4f13f6e99985036403da77734a025ee5

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In Applied Mathematics

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Citations in the corpus

Generalized Morrey spaces and trace operator (2016, methodology): “. The idea of replacing Lp(Rn) spaces with other function spaces are expanded in [18, 30, 44, 72]. Such attempts are made for Bσ-function spaces, variable Lebesgue spaces and Orlicz spaces. See [24], [35, 42] and [43], respectively. To recall the results, we use the notation based on [60]. Let f ∈ S”
New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, background): “Recently, new Hardy spaces of Musielak–Orlicz type have developed in many directions (see [11,47,50,56,57]), some their characterizations and applications were also established and studied in [11,27,38,50].”
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”
Characterizations of variable exponent Hardy spaces via Riesz transforms (2015, methodology): “In this article, we are devoted to extending conclusions of Theorem 1.1 to the variable exponent Hardy space Hp(·)(Rn) which was first studied by Nakai and Sawano [14] and, independently, by Cruz-Uribe and Wang [5].”
Besov-Type Spaces with Variable Smoothness and Integrability (2015, methodology): “(i) We point out that (2.4) and (2.5) are called the doubling condition and the compatibility condition, respectively, which have been used by Nakai [46, 47] and Nakai and Sawano [48] when they studied generalized Campanato spaces.”
Variable weak Hardy spaces and their applications (2016, methodology): “On the other hand, based on the variable Lebesgue space, several variable function spaces are developed rapidly in recent years (see, for example, [3, 4, 12, 14, 32, 41, 44, 45]).”
Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “[54] E. Nakai and Y. Sawano, Hardy spaces with variable exponents and generalized Campanato spaces, J. Funct.”
Variable Anisotropic Hardy Spaces and Their Applications (2017, methodology): “[83] C. Zhuo, Y. Sawano and D. Yang, Hardy spaces with variable exponents on RD-spaces and applications, Dissertationes Math.”
FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, methodology): “[154] If p(·) satisfies 0 < p− ≤ p+ < ∞, (14.”
Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, methodology): “We stress that an essential progress on variable Hardy space Hp(⋅)(Rn), defined by radial grand maximal functions, appeared in Nakai and Sawano [44].”
Martingale Hardy spaces with variable exponents (2014, methodology): “. We refer to Lemma 3.2 in [6] for this fact. The second aim of this paper is the atomic characterization of variable Hardy martingale spaces. Our result can be regarded as the probability version of [5, 22]; we do not use the log-Ho¨lder continuity of p(x) and it seems that our proofs are simpler b”