Interpolation of intersections of \(L_ p\) spaces (Q1822314)

Let \(0<p_ 1,p_ 2,p_ 3,p_ 4,q\leq \infty\) and \(0<\theta <1\). The interpolation spaces \([L_{p_ 1}\cap L_{p_ 2},L_{p_ 3}\cap L_{p_ 4}]_{\theta,q}\) are identified. Some results are also proved on interpolating intersections of Lorentz spaces. As an application a moment inequality is proved for sums of independent random variables in \(L_{p,q}\).