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The m-Hessian Operator on Some Weighted Energy Classes of Delta m-Subharmonic Functions

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Abstract

In this paper, we construct a topology on the vector space \(\delta \mathcal F_{m,\chi }(\Omega )\). We also prove that with this topology it is quasi-Banach, non-separable and non-reflexive. We also give a characterization for the class \(\mathcal F_{m, \min \{\chi _1, \chi _2\}}(\Omega )\).

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Acknowledgements

The authors gratefully acknowledges the many helpful suggestions of Professor Pham Hoang Hiep during the preparation of the paper. The author is also indebted to the referee for his useful comments that helped to improve the paper. This work was supported by the B2020-TTB-02 program.

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Authors and Affiliations

  1. Department of Mathematics, Tay Bac University, Sonla, Vietnam

    V. V. Hung

  2. Department of Mathematics, The University of Da Nang-University of Science and Education, Danang, Vietnam

    H. N. Quy

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  1. V. V. Hung
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  2. H. N. Quy
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Correspondence to V. V. Hung.

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Hung, V.V., Quy, H.N. The m-Hessian Operator on Some Weighted Energy Classes of Delta m-Subharmonic Functions. Results Math 75, 112 (2020). https://doi.org/10.1007/s00025-020-01242-z

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