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Hölder’s inequalities involving the infinite product and their applications in martingale spaces

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Abstract

We prove Hölder type inequalities for integrals and conditional expectations involving the infinite product. Moreover, a generalized Doob maximal operator is introduced and weighted inequalities for this operator are established.

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Authors and Affiliations

  1. School of Mathematical Sciences, Yangzhou University, 225002, Yangzhou, China

    W. Chen & L. B. Jia

  2. School of Mathematics and Statistics, Central South University, 410075, Changsha, China

    Y. Jiao

Authors
  1. W. Chen
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  2. L. B. Jia
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  3. Y. Jiao
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Corresponding author

Correspondence to W. Chen.

Additional information

The first author was supported by the National Natural Science Foundation of China (Grant No. 11101353), the Natural Science Foundation of Jiangsu Education Committee (Grant No. 11KJB110018), the Natural Science Foundation of Jiangsu Province (Grant Nos. BK2012682 and BK20141217) and the School Foundation of Yangzhou University (Grant No. 2015CXJ001).

The third author was supported by the National Natural Science Foundation of China (Grant No. 11471337).

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Chen, W., Jia, L.B. & Jiao, Y. Hölder’s inequalities involving the infinite product and their applications in martingale spaces. Anal Math 42, 121–141 (2016). https://doi.org/10.1007/s10476-016-0202-1

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  • DOI: https://doi.org/10.1007/s10476-016-0202-1

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