Some Extensions of Young Inequality in Integral Form

Young inequality is used widely in mathematical analysis and plays an important role in the development of modern mathematics.This paper discusses some extensions of Young inequality in integral form by combining mathematical analysis with theory of inequalities.The proof of equivalence between Young inequality and Young inverse inequality in integral form shows the inherent unity of Young inequality and compactness of the mathematical reasoning.The extensions of Young inverse inequality in integral form,as the latest developments of Young inequality,can be used in different mathematical fields,such as constructing dual space and proving Sobolev theorem.