Hilbert transforms in L2

ABSTRACT MSc. Thesis HİLBERT TRANSFORMS IN If Birol TOPÇU Afyon Kocatepe University Graduate School of Natural and Applied Sciences Department of Mathematics Supervisor : Assoc. Prof. Dr. Hüseyin YILDIRIM 1997, Page:39 Jury : Assoc. Prof. Dr. Hüseyin YILDIRIM Assoc. Prof. Dr. Ismail EKİNCİO?LU Assoc. Prof. Dr. Ismail ÖZKAN This thesis consists of three chapters. In the first chapter, we dealt with the basic concepts. In the second chapter, by defining the Hubert Transform which is required for our study, information about the Poison Kernel, definition of Poisson Integral, The Riezs Operator, Riezs Transform, Calderon-Zygmund Operator and Calderon-Zygmund Kernel were given. It was shown that in L2 space, almost everywhere, It was comparable a Poissn integral of Hubert Transform of a function with conjugate Poisson integral. In the third chapter, the multiplier operator, extension operator, the Singular integral Operator that was obtained by Calderon- Zygmund Kernels, and their specialities were defined. Consequently, a theorem Geometric Characterization of the Riezs Transforms were illustrated. KEYWORDS: Hubert Transform Calderon-Zygmund Kernel Calderon-Zygmund Operator Poisson Kernel Multiplier Operator Riezs Transform