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On pointwise interpolation inequalities for derivatives

Vladimir G. Maz'yaTatjana 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 k is the gradient of order k , 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 ( n ) W p l ( n ) ) is described.

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