Abstract
We investigate the real interpolation spaces between martingale Orlicz–Hardy spaces \(H_{\Phi}^s\) and martingale Hardy spaces \(H_{\infty}^s\) via atomic decomposition. Moreover, its corresponding weak version is also established.
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C. Bennett and R. Sharpley, Interpolation of Operators, Pure and Applied Mathematics, vol. 129, Academic Press, Inc. (Boston, MA, 1988)
J. Bergh and J. Lofstrom, Interpolation Spaces. An Introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag (Berlin–New York, 1976)
Byun, S., Yao, F., Zhou, S.: Gradient estimates in Orlicz space for nonlinear elliptic equations. J. Funct. Anal. 255, 1851–1873 (2008)
del Campo, R., Fernández, A., Manzano, A., Mayoral, F., Naranjo, F.: Complex interpolation of Orlicz spaces with respect to a vector measure. Math. Nachr. 287, 23–31 (2014)
L. Grafakos, Classical Fourier Analysis, second ed., Graduate Texts in Mathematics, vol. 249, Springer (New York, 2008)
Gustavsson, J., Peetre, J.: Interpolation of Orlicz spaces. Studia Math. 60, 33–59 (1977)
Hao, Z., Li, L.: Orlicz-Lorentz Hardy martingale spaces. J. Math. Anal. Appl. 482, 123520 (2020)
Jiao, Y.: Embeddings between weak Orlicz martingale spaces. J. Math. Anal. Appl. 378, 220–229 (2011)
Y. Jiao, W. Chen, and P. Liu, Interpolation on weak martingale Hardy space, Acta Math. Sin. (Engl. Ser.), 25 (2009), 1297–1304
Jiao, Y., Peng, L., Liu, P.: Interpolation for weak Orlicz spaces with \(M_{\Delta }\) condition. Sci. China Ser. A 51, 2072–2080 (2008)
Y. Jiao, F. Weisz, L. Wu, and D. Zhou, Real interpolation for variable martingale Hardy spaces, submission (2019)
Y. Jiao, L. Wu, and L. Peng, Weak Orlicz–Hardy martingale spaces, Internat. J. Math., 26 (2015), 1550062, pp. 26
J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I. Sequence spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92, Springer-Verlag (Berlin–New York, 1977)
Liu, K., Zhou, D., Peng, L.: A weak type John-Nirenberg theorem for martingales. Statist. Probab. Lett. 122, 190–197 (2017)
Liu, P., Hou, Y., Wang, M.: Weak Orlicz space and its applications to the martingale theory. Sci. China Math. 53, 905–916 (2010)
Miyamoto, T., Nakai, E., Sadasue, G.: Martingale Orlicz-Hardy spaces. Math. Nachr. 285, 670–686 (2012)
Nakai, E., Sawano, Y.: Orlicz-Hardy spaces and their duals. Sci. China Math. 57, 903–962 (2014)
S. Wang, D. Yang, W. Yuan, and Y. Zhang, Weak Hardy-type spaces associated with ball quasi-Banach function spaces. II: Littlewood–Paley characterizations and real interpolation, arXiv:1906.03653v1 (2019)
F. Weisz, Martingale Hardy Spaces and their Applications in Fourier Analysis, Lecture Notes in Mathematics, vo. 1568, Springer (1994)
Weisz, F., Weak martingale Hardy spaces, Probab. Math. Statist., 18, : Acta Univ. Wratislav. No. 2045, 133–148 (1998)
Xie, G., Weisz, F., Yang, D., Jiao, Y.: New martingale inequalities and applications to Fourier analysis. Nonlinear Anal. 182, 143–192 (2019)
Xie, G., Yang, D.: Atomic characterizations of weak martingale Musielak-Orlicz Hardy spaces and their applications. Banach J. Math. Anal. 13, 884–917 (2019)
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Long Long is supported by the Natural Science Foundation of China(Grant No. 11501580).
Hongli Tian is supported by the Fundamental Research Funds for the Central Universities of Central South University (No. 2019zzts116).
Dejian Zhou is supported by NSFC (11701574).
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Long, L., Tian, H. & Zhou, D. Interpolation of martingale Orlicz–Hardy spaces. Acta Math. Hungar. 163, 276–294 (2021). https://doi.org/10.1007/s10474-020-01097-4
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DOI: https://doi.org/10.1007/s10474-020-01097-4