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Dual spaces for variable martingale Lorentz–Hardy spaces

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Abstract

Let \(H_{p(\cdot ),q}\) be the variable Lorentz–Hardy martingale spaces. In this paper, we give a new atomic decomposition for these spaces via simple \(L_r\)-atoms \((1<r \le \infty )\). Using this atomic decomposition, we consider the dual spaces of variable Lorentz-Hardy spaces \(H_{p(\cdot ),q}\) for the case \(0<p(\cdot )\le 1\), \(0<q\le 1\), and \(0<p(\cdot )<2\), \(1<q<\infty \) respectively, and prove that they are equivalent to the BMO spaces with variable exponent. Furthermore, we also obtain several John-Nirenberg theorems based on the dual results.

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Acknowledgements

The authors would like to thank the anonymous reviewers for helpful suggestions.

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Authors and Affiliations

  1. School of Mathematics and statistics, Central South University, Changsha, 410083, China

    Yong Jiao, Lian Wu & Dejian Zhou

  2. Department of Numerical Analysis, Eötvös L. University, Pázmány P. sétány 1/C., 1117, Budapest, Hungary

    Ferenc Weisz

Authors
  1. Yong Jiao
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  2. Ferenc Weisz
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  3. Lian Wu
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  4. Dejian Zhou
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Corresponding author

Correspondence to Dejian Zhou.

Additional information

Communicated by Fedor Sukochev.

Ferenc Weisz was supported by the Hungarian National Research, Development and Innovation Office—NKFIH, KH130426. Dejian Zhou is supported by NSFC (11801573).

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Jiao, Y., Weisz, F., Wu, L. et al. Dual spaces for variable martingale Lorentz–Hardy spaces. Banach J. Math. Anal. 15, 53 (2021). https://doi.org/10.1007/s43037-021-00139-5

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  • DOI: https://doi.org/10.1007/s43037-021-00139-5

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