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- W2059775097 abstract "Landau-Kolmogorov inequalities have been extensively studied on both continuous and discrete domains for an entire century. However, the research is limited to the study of functions and sequences on $Bbb R$ and $Bbb Z$, with no equivalent inequalities in higher-dimensional spaces. The aim of this paper is to obtain a new class of discrete Landau-Kolmogorov type inequalities of arbitrary dimension: $$ |varphi|_{ell^infty(Bbb Z^d)} leq mu_{p,d}|nabla_Dvarphi|^{p/2^d}_{ell^2(Bbb Z^d)}, |varphi|^{1-p/2^d}_{ell^2(Bbb Z^d)}, % $$ where the constant $mu_{p,d}$ is explicitly specified. In fact, this also generalises the discrete Agmon inequality to higher dimension, which in the corresponding continuous case is not possible." @default.
- W2059775097 created "2016-06-24" @default.
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- W2059775097 date "2013-12-13" @default.
- W2059775097 modified "2023-09-27" @default.
- W2059775097 title "Agmon-Kolmogorov inequalities on $ell^2(Bbb Z^d)$" @default.
- W2059775097 hasPublicationYear "2013" @default.
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