SOME MULTI-SUBLINEAR OPERATORS ON GENERALIZED MORREY SPACES WITH NON-DOUBLING MEASURES

Title & Authors
SOME MULTI-SUBLINEAR OPERATORS ON GENERALIZED MORREY SPACES WITH NON-DOUBLING MEASURES
Shi, Yanlong; Tao, Xiangxing;

Abstract
In this paper the boundedness for a large class of multi-sublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calder$\small{\acute{o}}$n-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.
Keywords
multilinear Calder$\small{\acute{o}}$n-Zygmund operator;multilinear fractional integral;multi-sublinear maximal function;generalized Morrey spaces;non-doubling measure;
Language
English
Cited by
1.
Local Morrey and Campanato Spaces on Quasimetric Measure Spaces, Journal of Function Spaces, 2014, 2014, 1
2.
Necessary and sufficient conditions for boundedness of multilinear fractional integrals with rough kernels on Morrey type spaces, Journal of Inequalities and Applications, 2016, 2016, 1
3.
Generalized fractional maximal operators and vector-valued inequalities on generalized Orlicz–Morrey spaces, Revista Matemática Complutense, 2016, 29, 1, 59
4.
Boundedness and Compactness for the Commutators of Bilinear Operators on Morrey Spaces, Potential Analysis, 2015, 42, 3, 717
References
1.
L. Grafakos and R. Torres, Multilinear Calderon-Zygmund theory, Adv. Math. 165 (2002), no. 1, 124-164.

2.
C. E. Kenig and E. M. Stein, Multilinear estimates and fractional integration, Math. Res. Lett. 6 (1999), no. 1, 1-15.

3.
A. K. Lerner, S. Ombrosi, C. Perze, R. H. Torres, and R. R. Trujillo-Gonzaalez, New maximal functions and multiple weights for the multilinear Calderon-Zygmund theory, Adv. Math. 220 (2009), no. 4, 1222-1264.

4.
J. Lian and H. Wu, A class of commutators for multilinear fractional integrals in non-homogeneous spaces, J. Inequal. Appl. 2008 (2008), Article ID 373050, 17 pages.

5.
Y. Lin and S. Lu, Multilinear Calderon-Zygmund operator on Morrey type spaces, Anal. Theory Appl. 22 (2006), no. 4, 387-400.

6.
Y. Lin and S. Lu, Boundedness of multilinear singular integral operators on Hardy and Herz-type spaces, Hokkaido Math. J. 36 (2007), no. 3, 585-613.

7.
E. Nakai, Hardy-Littlewood maximal operator, singular integral operators and the Riesz potentials on generalized Morrey spaces, Math. Nachr. 166 (1994), no. 1, 95-103.

8.
Y. Sawano, Generalized Morrey spaces for non-doubling measures, Nonlinear Differential Equations Appl. 15 (2008), no. 4-5, 413-425.

9.
Y. Sawano and H. Tanaka, Morrey spaces for non-doubling measures, Acta Math. Sin. (Engl. Ser.) 21 (2005), no. 6, 1535-1544.

10.
Y. Shi and X. Tao, Boundedness for multilinear fractional integral operators on Herz type spaces, Appl. Math. J. Chinese Univ. Ser. B 23 (2008), no. 4, 437-446.

11.
Y. Shi and X. Tao, Multilinear Riesz potential operators on Herz-type spaces and generalized Morrey spaces, Hokkaido Math. J. 38 (2009), no. 4, 635-662.

12.
E. M. Stein, Harmonic Analysis: Real-Variable methods, Orthogonality, and Oscillatory Integrals, Princeton N. J. Princeton Univ Press, 1993.

13.
X. Tao, Y. Shi, and S. Zhang, Boundedness of multilinear Riesz potential on the product of Morrey and Herz-Morrey spaces, Acta Math. Sinica (Chin. Ser.) 52 (2009), no. 3, 535-548.

14.
X. Tolsa, BMO, \$H^{1}\$, and Calderon-Zygmund operators for nondoubling measures, Math. Ann. 319 (2001), no. 1, 89-149.

15.
J. Xu, Boundedness of multilinear singular integrals for non-doubling measures, J. Math. Anal. Appl. 327 (2007), no. 1, 471-480.