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Currently displaying 1 – 2 of 2

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On the spectrum of multipliers in Bessel potential spaces

Tatjana Olegovna Shaposhnikova — 1985

Časopis pro pěstování matematiky

On pointwise interpolation inequalities for derivatives

Vladimir G. Maz'ya; Tatjana Olegovna Shaposhnikova — 1999

Mathematica Bohemica

Pointwise interpolation inequalities, in particular, ku(x)c(Mu(x)) 1-k/m (Mmu(x))k/m, k<m, and |Izf(x)|c (MIf(x))Re z/Re (Mf(x))1-Re z/Re , 0<Re z<Re<n, where $\nabla_{k}$ is the gradient of order $k$ , $ℳ$ is the Hardy-Littlewood maximal operator, and $I_{z}$ is the Riesz potential of order $z$ , are proved. Applications to the theory of multipliers in pairs of Sobolev spaces are given. In particular, the maximal algebra in the multiplier space $M (W_{p}^{m} (ℝ^{n}) \to W_{p}^{l} (ℝ^{n}))$ is described.

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