Download or read book Interpolation Theorems and Applications to Singular Integrals written by Mervat Akram Madi and published by . This book was released on 2009 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new area in mathematics has evolved out of interest in singular integrals. Att empts were made to bound singular integral operators with respect to certain Lp norms. Having various kinds of singular integrals that differ in the number of v ariables, the characteristics of the phase function, the values of the parameter s involved, etc bears witness for applying diverse methods as differentiation an d interpolation methods, and also affects the range of p's for which these opera tors are bounded. Meanwhile, the flexible properties of Lorentz norms allowed a great progress in real and complex interpolation methods which have always been a significant approach to the problem. Our plan is to show how both real and complex interpolation techniques can be ap plied to bound singular integral operators. After acquiring a sufficient idea ab out Lorentz spaces and their properties, we are going first to demonstrate a rea l interpolation method (Wolff interpolation theorem), and present Hardy's Lp ine quality as an application to it; and second, to prove a complex interpolation th eorem (Stein- Weiss complex interpolation theorem) and apply it to a more sophis ticated singular integral operator.