Frontiers of Mathematics in China >
Hardy factorization in terms of fractional commutators in Lorentz spaces
Received date: 09 Mar 2021
Accepted date: 15 Jun 2021
Published date: 15 Oct 2022
Copyright
We provide a constructive proof of (the classical Hardy space) factorization in terms of fractional commutators in Lorentz spaces. As a direct application, we obtain a characterization of functions in BMO space. Furthermore, we also obtain a Lorentz compactness characterization of fractional commutators.
Key words: BMO; CMO; Lorentz space; commutator; Hardy space; Riesz potential
Nguyen Anh DAO . Hardy factorization in terms of fractional commutators in Lorentz spaces[J]. Frontiers of Mathematics in China, 2022 , 17(5) : 853 -873 . DOI: 10.1007/s11464-021-0946-1
1 |
Arai H, Mizuhara T. Morrey spaces on spaces of homogeneous type and estimates for □b and the Cauchy-Szegö projection. Math Nachr, 1997, 186: 5–20
|
2 |
Beatrous F, Li S Y. Boundedness and compactness of operators of Hankel type. J Funct Anal, 1993, 111: 350–379
|
3 |
Bramanti M, Cerutti M C. Commutators of singular integrals on homogeneous spaces. Boll Unione Mat Ital B (7), 1996, 10(4): 843–883
|
4 |
Brudnyi Y. Compactness criteria for spaces of measurable functions. St Petersburg Math J, 2015, 26: 49–68
|
5 |
Calderón A P, Zygmund A. Singular integral operators and differential equations. Amer J Math, 1957, 79: 901–921
|
6 |
Chanillo S. A note on commutators. Indiana Univ Math J, 1982, 31: 7–16
|
7 |
Chen Y, Ding Y, Wang X. Compactness of commutators of Riesz potential on Morrey spaces. Potential Anal, 2009, 30: 301–313
|
8 |
Chiarenza F, Frasca M, Longo P. Solvability of the Dirichlet problem for non divergence elliptic equations with VMO coefficients. Trans Amer Math Soc, 1993, 336: 841–853
|
9 |
Coifman R, Rochberg R, Weiss G. Factorization theorems for Hardy spaces in several variables. Ann of Math, 1976, 103(3): 611–635
|
10 |
Dafni G. Local VMO and weak convergence in h1. Canad Math Bull, 2002, 45: 46–59
|
11 |
Dao N A. Morrey boundedness and compactness characterizations of integral commutators with singular kernel on strictly pseudoconvex domains in ℂn. J Math Anal Appl, 2020, 492: 124483
|
12 |
Dao N A, Duong X T, Ha L K. Commutators of Cauchy-Fantappiè type integrals on generalized Morrey spaces on domains of complex ellipsoids. J Geom Anal (to appear)
|
13 |
Dao N A, Krantz S G. Lorentz boundedness and compactness characterization of integral commutators on spaces of homogeneous type. Nonlinear Anal, 2021, 203: 112162
|
14 |
Di Fazio G, Ragusa M A. Commutators and Morrey spaces. Boll Unione Mat Ital A (7), 1991, 5(3): 323–332
|
15 |
Hedberg L. On certain convolution inequalities. Proc Amer Math Soc, 1972, 36: 505–510
|
16 |
Iwaniec T, Sboedone C. Riesz transform and elliptic PDEs with VMO-coefficients. J Anal Math, 1998, 74: 183–212
|
17 |
Komori Y, Mizuhara T. Factorization of functions in H1(ℝn) and generalized Morrey spaces. Math Nachr, 2006, 279(5-6): 619–624
|
18 |
Komori Y, Shirai S. Weighted Morrey spaces and a singular integral operator. Math Nachr, 2009, 282(2): 219–231
|
19 |
Krantz S G, Li S Y. Boundedness and compactness of integral operators on spaces of homogeneous type and applications II. J Math Anal Appl, 2001, 258: 642–657
|
20 |
O’Neil R. Convolution operators and L(p; q) spaces. Duke Math J, 1963, 30: 129–142
|
21 |
Stein E M. Singular Integrals and Differentiability Properties of Functions. Princeton Math Ser, No 30. Princeton: Princeton Univ Press, 1970
|
22 |
Tao J, Yang D C, Yang D Y. Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces. Math Methods Appl Sci, 2019, 42(5): 1631–1651
|
23 |
Uchiyama A. On the compactness of operators of Hankel type. Tohoku Math J, 1978, 30: 163–171
|
/
〈 | 〉 |