Suppose \(1<p<q<r<\infty \). (Here \(p\) and \(q\) are arbitrary, not necessarily conjugate.) Prove that \(L^p(\mathbb R)\cap L^r(\mathbb R)\subset L^q(\mathbb R)\).
Question
Math 6210 • Real Analysis
Fall 2010 • Question 4
Question
Fall 2010 • Question 4
Suppose \(1<p<q<r<\infty \). (Here \(p\) and \(q\) are arbitrary, not necessarily conjugate.) Prove that \(L^p(\mathbb R)\cap L^r(\mathbb R)\subset L^q(\mathbb R)\).