We prove inequalities for the Riesz means for the discrete spectra of selfadjoint compact integral operators in some class. Such bounds imply inequalities for the counting function of the Dirichlet boundary problem for the Laplace operator.
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Translated from Problemy Matematicheskogo Analiza99, 2019, pp. 35-45.
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Laptev, A., Velicu, A. Spectral Inequalities for a Class of Integral Operators. J Math Sci 242, 214–226 (2019). https://doi.org/10.1007/s10958-019-04475-8
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DOI: https://doi.org/10.1007/s10958-019-04475-8