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Maximal \({\gamma}\)-regularity

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Abstract

In this paper, we prove maximal regularity estimates in “square function spaces” which are commonly used in harmonic analysis, spectral theory, and stochastic analysis. In particular, they lead to a new class of maximal regularity results for both deterministic and stochastic equations in L p-spaces with \({1 < p < {\infty} }\). For stochastic equations, the case 1 < p < 2 was not covered in the literature so far. Moreover, the “square function spaces” allow initial values with the same roughness as in the L 2-setting.

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Authors and Affiliations

  1. Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    Jan van Neerven & Mark Veraar

  2. Institut für Analysis, Universität Karlsruhe (TH), 76128, Karlsruhe, Germany

    Lutz Weis

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  1. Jan van Neerven
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  2. Mark Veraar
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  3. Lutz Weis
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Correspondence to Jan van Neerven.

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The first named author is supported by VICI subsidy 639.033.604 of the Netherlands Organisation for Scientific Research (NWO). The second author is supported by VENI subsidy 639.031.930 of the Netherlands Organisation for Scientific Research (NWO). The third named author is supported by a grant from the Deutsche Forschungsgemeinschaft (We 2847/1-2).

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van Neerven, J., Veraar, M. & Weis, L. Maximal \({\gamma}\)-regularity. J. Evol. Equ. 15, 361–402 (2015). https://doi.org/10.1007/s00028-014-0264-0

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