ENDPOINT ESTIMATES FOR MAXIMAL COMMUTATORS IN NON-HOMOGENEOUS SPACES

Title & Authors
ENDPOINT ESTIMATES FOR MAXIMAL COMMUTATORS IN NON-HOMOGENEOUS SPACES
Hu, Guoen; Meng, Yan; Yang, Dachun;

Abstract
Certain weak type endpoint estimates are established for maximal commutators generated by $\small{Calder\acute{o}n-Zygmund}$ operators and $\small{Osc_{exp}L^{\gamma}({\mu})}$ functions for $\small{{\gamma}{\ge}1}$ under the condition that the underlying measure only satisfies some growth condition, where the kernels of $\small{Calder\acute{o}n-Zygmund}$ operators only satisfy the standard size condition and some $\small{H\ddot{o}rmander}$ type regularity condition, and $\small{Osc_{exp}L^{\gamma}({\mu})}$ are the spaces of Orlicz type satisfying that $\small{Osc_{exp}L^{\gamma}({\mu})}$
Keywords
$\small{Calder\acute{o}n}$-Zygmund operator;$\small{Osc_{exp}L^r({\mu})}$;maximal commutator;endpoint estimate;
Language
English
Cited by
References
1.
G. Hu, Y. Meng, and D. Yang, Multilinear commutators of singular integrals with non doubling measures, Integral Equations Operator Theory 51 (2005), no. 2, 235-255

2.
G. Hu, Y. Meng, and D. Yang, Estimates for maximal singular integral operators in non-homogeneous spaces, Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), no. 2, 351-364

3.
G. Hu, Y. Meng, and D. Yang, Endpoint estimate for maximal commutators with non-doubling measures, Acta Math. Sci. Ser. B Engl. Ed. 26 (2006), no. 2, 271-280

4.
G. Hu, Y. Meng, and D. Yang, Boundedness of some maximal commutators in Hardy-type spaces with non-doubling measures, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 6, 1129-1148

5.
F. Nazarov, S. Treil, and A. Volberg, Accretive system Tb-theorems on nonhomogeneous spaces, Duke Math. J. 113 (2002), no. 2, 259-312

6.
F. Nazarov, S. Treil, and A. Volberg, Tb-theorem on nonhomogeneous spaces, Acta Math. 190 (2003), 151-239

7.
J. Orobitg and C. Perez, Ap weights for nondoubling measures in $R^n$ and applications, Trans. Amer. Math. Soc. 354 (2002), no. 5, 2013-2033

8.
C. Perez and R. Trujillo-Gonzalez, Sharp weighted estimates for multilinear commutators, J. London Math. Soc. 65 (2002), no. 3, 672-692

9.
X. Tolsa, BMO, $H^1$, and Calderon-Zygmund operators for non doubling measures, Math. Ann. 319 (2001), no. 1, 89-149

10.
X. Tolsa, A T(1) theorem for non-doubling measures with atoms, Proc. London Math. Soc. (3) 82 (2001), no. 1, 195-228

11.
X. Tolsa, Littlewood-Paley theory and the T(1) theorem with non-doubling measures, Adv. Math. 164 (2001), no. 1, 57-116

12.
X. Tolsa, The space $H^1$ for nondoubling measures in terms of a grand maximal operator, Trans. Amer. Math. Soc. 355 (2003), no. 1, 315-348

13.
X. Tolsa, Painleve's problem and the semiadditivity of analytic capacity, Acta Math. 190 (2003), 105-149

14.
J. Verdera, The fall of the doubling condition in Calderon-Zygmund theory, Publ. Mat. Vol. Extra (2002), 275-292