About:Interpolation inequality

In the field of mathematical analysis, an interpolation inequality is an inequality of the form where for , is an element of some particular vector space equipped with norm and is some real exponent, and is some constant independent of . The vector spaces concerned are usually function spaces, and many interpolation inequalities assume and so bound the norm of an element in one space with a combination norms in other spaces, such as Ladyzhenskaya's inequality and the Gagliardo-Nirenberg interpolation inequality, both given below. Nonetheless, some important interpolation inequalities involve distinct elements , including Hölder's Inequality and Young's inequality for convolutions which are also presented below.