Weighted boundedness of multilinear Calderón commutators
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Yanping Chen
Abstract
The main result of this paper is to give that if
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11871096
Award Identifier / Grant number: 11471033
Funding statement: The project was in part supported by NSF of China (No. 11871096, No. 11471033).
Acknowledgements
The authors would like to express their deep gratitude to the referee for giving many valuable suggestions, which greatly improved the exposition of the paper.
References
[1] J. Álvarez, R. J. Bagby, D. S. Kurtz and C. Pérez, Weighted estimates for commutators of linear operators, Studia Math. 104 (1993), no. 2, 195–209. 10.4064/sm-104-2-195-209Suche in Google Scholar
[2]
M. Bramanti and M. C. Cerutti,
[3] A.-P. Calderón, Commutators of singular integral operators, Proc. Natl. Acad. Sci. USA 53 (1965), 1092–1099. 10.1073/pnas.53.5.1092Suche in Google Scholar PubMed PubMed Central
[4] A.-P. Calderón, Commutators, singular integrals on Lipschitz curves and applications, Proceedings of the International Congress of Mathematicians (Helsinki 1978), Academia Scientiarum Fennica, Helsinki (1980), 85–96. Suche in Google Scholar
[5] A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85–139. 10.1007/978-94-009-1045-4_3Suche in Google Scholar
[6] A. P. Calderón and A. Zygmund, On a problem of Mihlin, Trans. Amer. Math. Soc. 78 (1955), 209–224. 10.1007/978-94-009-1045-4_7Suche in Google Scholar
[7] A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math. 78 (1956), 289–309. 10.1090/pspum/010Suche in Google Scholar
[8] A.-P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901–921. 10.1007/978-94-009-1045-4_15Suche in Google Scholar
[9]
Y. Chen and Y. Ding,
[10]
Y. Chen, Y. Ding and R. Li,
[11]
Y. Chen and L. Wang,
[12] Y. Chen and K. Zhu, Weighted norm inequality for the singular integral with variable kernel and fractional differentiation, J. Math. Anal. Appl. 423 (2015), no. 2, 1610–1629. 10.1016/j.jmaa.2014.10.074Suche in Google Scholar
[13]
F. Chiarenza, M. Frasca and P. Longo,
Interior
[14] G. Di Fazio and M. A. Ragusa, Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients, J. Funct. Anal. 112 (1993), no. 2, 241–256. 10.1006/jfan.1993.1032Suche in Google Scholar
[15] J. Duoandikoetxea, Fourier Analysis, Grad. Stud. Mathe. 29, American Mathematical Society, Providence, 2001. Suche in Google Scholar
[16] L. Grafakos, Modern Fourier Analysis, 3rd ed., Grad. Texts in Math. 250, Springer, New York, 2014. 10.1007/978-1-4939-1230-8Suche in Google Scholar
[17] S. Hofmann, Weighted inequalities for commutators of rough singular integrals, Indiana Univ. Math. J. 39 (1990), no. 4, 1275–1304. 10.1512/iumj.1990.39.39057Suche in Google Scholar
[18] C. B. Morrey, Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), no. 1, 126–166. 10.1090/S0002-9947-1938-1501936-8Suche in Google Scholar
[19] D. K. Palagachev and L. G. Softova, Singular integral operators, Morrey spaces and fine regularity of solutions to PDE’s, Potential Anal. 20 (2004), no. 3, 237–263. 10.1023/B:POTA.0000010664.71807.f6Suche in Google Scholar
[20] C. Pérez, Sharp estimates for commutators of singular integrals via iterations of the Hardy–Littlewood maximal function, J. Fourier Anal. Appl. 3 (1997), no. 6, 743–756. 10.1007/BF02648265Suche in Google Scholar
[21] C. Pérez and R. Trujillo-González, Sharp weighted estimates for multilinear commutators, J. Lond. Math. Soc. (2) 65 (2002), no. 3, 672–692. 10.1112/S0024610702003174Suche in Google Scholar
[22] S. L. Sobolev, On a theorem of functional analysis, Mat. Sb. 4 (1938), 471–497. 10.1090/trans2/034/02Suche in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Lower bounds for regular genus and gem-complexity of PL 4-manifolds with boundary
- Free cyclic group actions on highly-connected 2n-manifolds
- The distinction problems for Sp4 and SO3,3
- Affine cones over cubic surfaces are flexible in codimension one
- Permutations of zero-sumsets in a finite vector space
- On the finiteness of solutions for polynomial-factorial Diophantine equations
- Galois action on Fuchsian surface groups and their solenoids
- On a Lévy process pinned at random time
- Borsuk–Ulam theorem for filtered spaces
- A non-commutative differential module approach to Alexander modules
- Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: generic behavior
- Quantum modularity of partial theta series with periodic coefficients
- Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian
- Zeros of GL2 𝐿-functions on the critical line
- Weighted boundedness of multilinear Calderón commutators
- Two characterizations of central BMO space via the commutators of Hardy operators
- Weyl 𝑛-algebras and the Swiss cheese operad
- Syzygies in equivariant cohomology in positive characteristic
- Epsilon factors of symplectic type characters in the wild case
Artikel in diesem Heft
- Frontmatter
- Lower bounds for regular genus and gem-complexity of PL 4-manifolds with boundary
- Free cyclic group actions on highly-connected 2n-manifolds
- The distinction problems for Sp4 and SO3,3
- Affine cones over cubic surfaces are flexible in codimension one
- Permutations of zero-sumsets in a finite vector space
- On the finiteness of solutions for polynomial-factorial Diophantine equations
- Galois action on Fuchsian surface groups and their solenoids
- On a Lévy process pinned at random time
- Borsuk–Ulam theorem for filtered spaces
- A non-commutative differential module approach to Alexander modules
- Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: generic behavior
- Quantum modularity of partial theta series with periodic coefficients
- Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian
- Zeros of GL2 𝐿-functions on the critical line
- Weighted boundedness of multilinear Calderón commutators
- Two characterizations of central BMO space via the commutators of Hardy operators
- Weyl 𝑛-algebras and the Swiss cheese operad
- Syzygies in equivariant cohomology in positive characteristic
- Epsilon factors of symplectic type characters in the wild case
