|
|
Pure Mathematics 2023
极大算子的交换子在 Morrey 空间的有界性以及对 Lipschitz 空间的刻画
|
Abstract:
设M为Hardy-Littlewood 极大算子，M#为sharp 极大算子，b是局部可积函数。本文考虑了当b属于 Lipschitz 空间时，M 和M#与b生成的极大交换子和非线性交换子在 Morrey 空间中的有界性，并给出了 Lipschitz 空间的一些新等价刻画。
Let M be the Hardy-Littlewood maximal operator, M# be the sharp maximal operator
and b be a locally integrable function. In this paper, we consider the boundedness of maximal and nonlinear commutators generated by M and M# with b on Morrey spaces when b belongs to the Lipschitz spaces, by which some new characterizations of the Lipschitz spaces are given.
| [1] | Coifman, R.R., Rochberg, R. and Weiss, G. (1976) Factorization Theorems for Hardy Spaces
in Several Variables. Annals of Mathematics, 103, 611-635. https://doi.org/10.2307/1970954 |
| [2] | Janson, S. (1978) Mean Oscillation and Commutators of Singular Integral Operators. Arkiv
for Matematik, 16, 263-270. https://doi.org/10.1007/BF02386000 |
| [3] | Paluszynski, M. (1995) Characterization of the Besov Spaces via the Commutator Operator
of Coifman, Rochberg and Weiss. Indiana University Mathematics Journal, 44, 1-18.
https://doi.org/10.1512/iumj.1995.44.1976 |
| [4] | Agcayazi, M., Gogatishvili, A., Koca, K. and Mustafayev, R. (2015) A Note on Maximal
Commutators and Commutators of Maximal Functions. Journal of the Mathematical Society
of Japan, 67, 581-593. https://doi.org/10.2969/jmsj/06720581 |
| [5] | Bastero, J., Milman, M. and Ruiz, F. (2000) Commutators for the Maximal and Sharp Functions.
Proceedings of the American Mathematical Society, 128, 3329-3334.
https://doi.org/10.1090/S0002-9939-00-05763-4 |
| [6] | Fan, Y. and Jia, H.Y. (2012) Boundedness of Commutators of Maximal Function on Morrey
Space. Acta Mathematica Sinica, Chinese Series, 55, 701-706. |
| [7] | Guliyev, V.S. and Deringoz, F. (2018) Some Characterizations of Lipschitz Spaces via Commutators
on Generalized Orlicz-Morrey Spaces. Mediterranean Journal of Mathematics, 15,
Article No. 180. https://doi.org/10.1007/s00009-018-1226-5 |
| [8] | Milman, M. and Schonbek, T. (1990) Second Order Estimates in Interpolation Theory and
Applications. Proceedings of the American Mathematical Society, 110, 961-969.
https://doi.org/10.1090/S0002-9939-1990-1075187-4 |
| [9] | Xie, C. (2011) Some Estimates of Commutators. Real Analysis Exchange, 36, 405-416.
https://doi.org/10.14321/realanalexch.36.2.0405 |
| [10] | Zhang, P. and Wu, J.L. (2014) Commutators for the Maximal Functions on Lebesgue Spaces
with Variable Exponent. Mathematical Inequalities Applications, 17, 1375-1386.
https://doi.org/10.7153/mia-17-101 |
| [11] | Zhang, P. (2017) Characterization of Lipschitz Spaces via Commutators of the Hardy-
Littlewood Maximal Function. Comptes Rendus Mathematique, 355, 336-344.
https://doi.org/10.1016/j.crma.2017.01.022 |
| [12] | Zhang, P., Si, Z. and Wu, J. (2019) Some Notes on Commutators of the Fractional Maximal
Function on Variable Lebesgue Spaces. Journal of Inequalities and Applications, 2019, Article
No. 9. https://doi.org/10.1186/s13660-019-1960-7 |
| [13] | Zhang, P. (2019) Characterization of Boundedness of Some Commutators of Maximal Functions
in Terms of Lipschitz Spaces. Analysis and Mathematical Physics, 9, 1411-1427.
https://doi.org/10.1007/s13324-018-0245-5 |
| [14] | Morrey, C.B. (1938) On the Solutions of Quasi-Linear Elliptic Partial Differential Equations.
Transactions of the American Mathematical Society, 43, 126-166.
https://doi.org/10.1090/S0002-9947-1938-1501936-8 |
| [15] | Peetre, J. (1969) On the Theory of Lp,λ Spaces. Journal of Functional Analysis, 4, 71-87.
https://doi.org/10.1016/0022-1236(69)90022-6 |
| [16] | Zhang P, Wu J L and Sun J. (2018) Commutators of Some Maximal Functions with Lipschitz
Function on Orlicz Spaces. Mediterranean Journal of Mathematics, 15, Article No. 216.
https://doi.org/10.1007/s00009-018-1263-0 |
| [17] | Komori Y and Mizuhara T. (2003) Notes on Commutators and Morrey Spaces. Hokkaido
Mathematical Journal, 32, 345-353. https://doi.org/10.14492/hokmj/1350657528 |
| [18] | Zhang P and Wu J L. (2009) Commutators of the Fractional Maximal Functions. Acta Math-
ematica Sinica, Chinese Series, 52, 1235-1238. |
| [19] | Chiarenza F. (1987) Morrey Spaces and Hardy-Littlewood Maximal Function. Rendiconti di
Matematica e delle sue Applicazioni, 7, 273-279. |
