Interpolation of linear operators in Lebesgue spaces with mixed norm (Q1074799)

The aim of this paper is to show that a bounded linear operator in the Lebesgue spaces \(L^ t(M^ n;L^ s(R^ m))\) with mixed norm is bounded in the usual Lebesgue space \(L^ u(M^{m+n})\) under a condition on (s,t), where \(l/u=(m/s+n/t)/(m+n)\). As applications of result on Riesz-Bochner summing operator and an inequality on the restriction problem of Fourier transform are shown. A detailed proof will be found in Tôhoku Math. J. 38, 469-490 (1986).