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Variation operators for semigroups and Riesz transforms acting on weighted \(L^p\) and BMO spaces in the Schrödinger setting

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Abstract

In this paper, we extend the results of Schrödinger type operators (Betancor et al., Rev Mat Complut 26:485–534, 2013) and (Betancor et al., Potential Anal 38:711–739, 2013) to the weighted \({L^p({{\mathbb {R}}^{n}})}\) and \(\mathrm{BMO}\) spaces respectively, with the new type weight class defined (Bongioanni et al., J Math Anal Appl 373:563–579, 2011) which includes the Muckenhoupt class.

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Acknowledgments

The authors would like to thank the referees for some very valuable suggestions.

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

    Lin Tang & Qian Zhang

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  1. Lin Tang
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  2. Qian Zhang
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Correspondence to Lin Tang.

Additional information

The research was supported by the NNSF (11271024) and (11571289) of China.

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Tang, L., Zhang, Q. Variation operators for semigroups and Riesz transforms acting on weighted \(L^p\) and BMO spaces in the Schrödinger setting. Rev Mat Complut 29, 559–621 (2016). https://doi.org/10.1007/s13163-016-0199-9

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  • DOI: https://doi.org/10.1007/s13163-016-0199-9

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