A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces

By Dachun Yang, Yuan Zhou. 2009

95 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cae328f93397c2fe18737e1560789710aefa3832

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. Luong Dang Ky
4. Yuan Zhou
5. Yangyang Zhang
6. Songbai Wang
7. Baode Li
8. Jun Liu

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Luong Dang Ky
4. Yuan Zhou
5. Yangyang Zhang
6. Songbai Wang
7. Baode Li
8. Marcin Bownik

Citations in the corpus

• Localized Hardy Spaces $H^1$ Related to Admissible Functions on RD-Spaces and Applications to Schr\ (2009, result): “See [3, 55, 38, 21] for further details and examples.”
• Real-variable characterizations of Orlicz-slice Hardy spaces (2018, background): “Next we recall the notion of γ-quasi-Banach spaces (see, for example, [27], [44], [47] and [46]).”
• Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators (2008, methodology): “This extends both the results of Meda-Sj¨ ogren-Vallarino [24] and Yang-Zhou [ 41 ].”
• On Function Spaces with Mixed Norms — A Survey (2019, unknown): “and, for any ψ, φ∈Y , ‖T(ψ)−T(φ)‖Bγ ≤C‖T(ψ−φ)‖Bγ (see [42, 56, 81–83]).”
• H1 and BMO for certain locally doubling metric measures spaces (2009, background): “The problem of giving sufficient conditions for an operator uniformly bounded on atoms to extend to a bounded operator from H 1 (λ) to L 1 (λ) has been considered independently in [36, 47].”
• Weighted anisotropic product Hardy spaces and boundedness of sublinear operators (2009, methodology): “Using the Lusin-area function characterization of classical Hardy spaces, it was proved in [64] that if a sublinear operator T maps all smooth (p, 2, s)-atoms into uniformly bounded elements of a quasi-Banach space B, then T uniquely extends to a bounded sublinear operator from Hp(Rn) to B.”
• New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, methodology): “Then, we consider generalized quasi-Banach spaces which generalize the notion of quasi-Banach spaces in [59] (see also [9]), and obtain criterious for boundedness of sublinear operators on H(R).”
• Anisotropic Hardy-Lorentz spaces and their applications (2015, unknown): “This extends the corresponding results of Meda et al. [50], Yang-Zhou [74] and Grafakos et al. [36] to the present setting.”
• Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, unknown): “i=1 |μi| ‖T ( fi)‖γBγ and, for any f , g ∈ Y, ‖T ( f ) − T (g)‖Bγ ≤ C‖T ( f − g)‖Bγ (see [81, 82, 44, 79]).”