November  2016, 15(6): 2135-2160. doi: 10.3934/cpaa.2016031

Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated to non-negative self-adjoint operators satisfying Gaussian estimates

1. 

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex systems, Ministry of Education, Beijing 100875

2. 

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received  December 2015 Revised  May 2016 Published  September 2016

Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $\varphi:\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that $\varphi(x,\cdot)$ is an Orlicz function and $\varphi(\cdot,t)\in {\mathbb A}_{\infty}(\mathbb{R}^n)$ (the class of uniformly Muckenhoupt weights). Let $H_{\varphi,L}(\mathbb{R}^n)$ be the Musielak-Orlicz-Hardy space introduced via the Lusin area function associated with the heat semigroup of $L$. In this article, the authors obtain several maximal function characterizations of the space $H_{\varphi,L}(\mathbb{R}^n)$, which, especially, answer an open question of L. Song and L. Yan under an additional mild assumption satisfied by Schrödinger operators on $\mathbb{R}^n$ with non-negative potentials belonging to the reverse Hölder class, and second-order divergence form elliptic operators on $\mathbb{R}^n$ with bounded measurable real coefficients.
Citation: Dachun Yang, Sibei Yang. Maximal function characterizations of Musielak-Orlicz-Hardy spaces associated to non-negative self-adjoint operators satisfying Gaussian estimates. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2135-2160. doi: 10.3934/cpaa.2016031
References:
[1]

Unpublished Manuscript, 2005. Google Scholar

[2]

J. Funct. Anal., 201 (2003), 148-184. doi: 10.1016/S0022-1236(03)00059-4.  Google Scholar

[3]

Astérisque, 249 (1998), viii+172 pp.  Google Scholar

[4]

Anal. Geom. Metr. Spaces, 1 (2013), 69-129.  Google Scholar

[5]

Adv. Math., 229 (2012), 501-530. doi: 10.1016/j.aim.2011.09.007.  Google Scholar

[6]

Adv. Math., 25 (1977), 216-225.  Google Scholar

[7]

Commun. Pure Appl. Anal., 13 (2014), 1435-1463. doi: 10.3934/cpaa.2014.13.1435.  Google Scholar

[8]

Anal. Appl. (Singap.), (2015). doi: 10.1142/S0219530515500189.  Google Scholar

[9]

J. Cao, S. Mayboroda and D. Yang, Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators,, \emph{Forum Math.}, ().  doi: 10.1515/forum-2014-0127.  Google Scholar

[10]

Trans. Amer. Math. Soc., 347 (1995), 2941-2960. doi: 10.2307/2154763.  Google Scholar

[11]

J. Funct. Anal., 264 (2013), 1409-1437. doi: 10.1016/j.jfa.2013.01.006.  Google Scholar

[12]

in Fourier analysis and related topics, Banach Center Publ., 56, Polish Acad. Sci., Warsaw, (2002), 45-53.  Google Scholar

[13]

Acta Math., 129 (1972), 137-193.  Google Scholar

[14]

Second edition, Graduate Texts in Mathematics 250, Springer, New York, 2009. doi: 10.1007/978-0-387-09434-2.  Google Scholar

[15]

Mem. Amer. Math. Soc., 214 (2011), no. 1007, vi+78 pp. doi: 10.1090/S0065-9266-2011-00624-6.  Google Scholar

[16]

Math. Ann., 344 (2009), 37-116. doi: 10.1007/s00208-008-0295-3.  Google Scholar

[17]

Commun. Contemp. Math., 15 (2013), no. 6, 1350029, 37 pp. doi: 10.1142/S0219199713500296.  Google Scholar

[18]

J. Funct. Anal., 258 (2010), 1167-1224. doi: 10.1016/j.jfa.2009.10.018.  Google Scholar

[19]

Commun. Contemp. Math., 13 (2011), 331-373. doi: 10.1142/S0219199711004221.  Google Scholar

[20]

Forum Math., 24 (2012), 471-494. doi: 10.1515/form.2011.067.  Google Scholar

[21]

Rev. Mat. Iberoam., 3 (1987), 249-273. doi: 10.4171/RMI/50.  Google Scholar

[22]

Integral Equations Operator Theory, 78 (2014), 115-150. doi: 10.1007/s00020-013-2111-z.  Google Scholar

[23]

Trans. Amer. Math. Soc., 365 (2013), 2931-2958. doi: 10.1090/S0002-9947-2012-05727-8.  Google Scholar

[24]

J. Funct. Anal., 265 (2013), 2709-2723. doi: 10.1016/j.jfa.2013.08.003.  Google Scholar

[25]

Lecture Notes in Math. 1034, Springer-Verlag, Berlin, 1983. doi: 10.1007/BFb0072210.  Google Scholar

[26]

Marcel Dekker, Inc., New York, 1991. doi: 10.1080/03601239109372748.  Google Scholar

[27]

J. Funct. Anal., 259 (2010), 1466-1490. doi: 10.1016/j.jfa.2010.05.015.  Google Scholar

[28]

Adv. Math., 287 (2016), 463-484. doi: 10.1016/j.aim.2015.09.026.  Google Scholar

[29]

Princeton Univ. Press, Princeton, NJ, 1993.  Google Scholar

[30]

Acta Math., 103 (1960), 25-62.  Google Scholar

[31]

Trans. Amer. Math. Soc., 360 (2008), 4383-4408. doi: 10.1090/S0002-9947-08-04476-0.  Google Scholar

[32]

Front. Math. China, 10 (2015), 1203-1232. doi: 10.1007/s11464-015-0432-8.  Google Scholar

[33]

Indiana Univ. Math. J., 61 (2012), 81-129. doi: 10.1512/iumj.2012.61.4535.  Google Scholar

[34]

J. Geom. Anal., 24 (2014), 495-570. doi: 10.1007/s12220-012-9344-y.  Google Scholar

show all references

References:
[1]

Unpublished Manuscript, 2005. Google Scholar

[2]

J. Funct. Anal., 201 (2003), 148-184. doi: 10.1016/S0022-1236(03)00059-4.  Google Scholar

[3]

Astérisque, 249 (1998), viii+172 pp.  Google Scholar

[4]

Anal. Geom. Metr. Spaces, 1 (2013), 69-129.  Google Scholar

[5]

Adv. Math., 229 (2012), 501-530. doi: 10.1016/j.aim.2011.09.007.  Google Scholar

[6]

Adv. Math., 25 (1977), 216-225.  Google Scholar

[7]

Commun. Pure Appl. Anal., 13 (2014), 1435-1463. doi: 10.3934/cpaa.2014.13.1435.  Google Scholar

[8]

Anal. Appl. (Singap.), (2015). doi: 10.1142/S0219530515500189.  Google Scholar

[9]

J. Cao, S. Mayboroda and D. Yang, Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators,, \emph{Forum Math.}, ().  doi: 10.1515/forum-2014-0127.  Google Scholar

[10]

Trans. Amer. Math. Soc., 347 (1995), 2941-2960. doi: 10.2307/2154763.  Google Scholar

[11]

J. Funct. Anal., 264 (2013), 1409-1437. doi: 10.1016/j.jfa.2013.01.006.  Google Scholar

[12]

in Fourier analysis and related topics, Banach Center Publ., 56, Polish Acad. Sci., Warsaw, (2002), 45-53.  Google Scholar

[13]

Acta Math., 129 (1972), 137-193.  Google Scholar

[14]

Second edition, Graduate Texts in Mathematics 250, Springer, New York, 2009. doi: 10.1007/978-0-387-09434-2.  Google Scholar

[15]

Mem. Amer. Math. Soc., 214 (2011), no. 1007, vi+78 pp. doi: 10.1090/S0065-9266-2011-00624-6.  Google Scholar

[16]

Math. Ann., 344 (2009), 37-116. doi: 10.1007/s00208-008-0295-3.  Google Scholar

[17]

Commun. Contemp. Math., 15 (2013), no. 6, 1350029, 37 pp. doi: 10.1142/S0219199713500296.  Google Scholar

[18]

J. Funct. Anal., 258 (2010), 1167-1224. doi: 10.1016/j.jfa.2009.10.018.  Google Scholar

[19]

Commun. Contemp. Math., 13 (2011), 331-373. doi: 10.1142/S0219199711004221.  Google Scholar

[20]

Forum Math., 24 (2012), 471-494. doi: 10.1515/form.2011.067.  Google Scholar

[21]

Rev. Mat. Iberoam., 3 (1987), 249-273. doi: 10.4171/RMI/50.  Google Scholar

[22]

Integral Equations Operator Theory, 78 (2014), 115-150. doi: 10.1007/s00020-013-2111-z.  Google Scholar

[23]

Trans. Amer. Math. Soc., 365 (2013), 2931-2958. doi: 10.1090/S0002-9947-2012-05727-8.  Google Scholar

[24]

J. Funct. Anal., 265 (2013), 2709-2723. doi: 10.1016/j.jfa.2013.08.003.  Google Scholar

[25]

Lecture Notes in Math. 1034, Springer-Verlag, Berlin, 1983. doi: 10.1007/BFb0072210.  Google Scholar

[26]

Marcel Dekker, Inc., New York, 1991. doi: 10.1080/03601239109372748.  Google Scholar

[27]

J. Funct. Anal., 259 (2010), 1466-1490. doi: 10.1016/j.jfa.2010.05.015.  Google Scholar

[28]

Adv. Math., 287 (2016), 463-484. doi: 10.1016/j.aim.2015.09.026.  Google Scholar

[29]

Princeton Univ. Press, Princeton, NJ, 1993.  Google Scholar

[30]

Acta Math., 103 (1960), 25-62.  Google Scholar

[31]

Trans. Amer. Math. Soc., 360 (2008), 4383-4408. doi: 10.1090/S0002-9947-08-04476-0.  Google Scholar

[32]

Front. Math. China, 10 (2015), 1203-1232. doi: 10.1007/s11464-015-0432-8.  Google Scholar

[33]

Indiana Univ. Math. J., 61 (2012), 81-129. doi: 10.1512/iumj.2012.61.4535.  Google Scholar

[34]

J. Geom. Anal., 24 (2014), 495-570. doi: 10.1007/s12220-012-9344-y.  Google Scholar

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