Meskhi (A. Razmadze Mathematical Institute, Tbilisi, Georgia) systematically and in great detail analyzes a class of specific integral operators from the boundedness/compactness or non-compactness point of view, emphasizing important tools for solving a variety of problems in several areas of mathematics and its applications. The problems related estimating the measure of the non-compactness for differential and integral operations acting between Banach spaces, he says, are closely connected with eigenvalue estimates and other spectral properties for these operators. After setting out the basic ingredients, he covers maximal operators, kernel operators on cones, potential and identity operators, generalized one-sided potentials in Lp(x) spaces, and singular integrals. He posits readers ranging from researchers in functional and harmonic analysis to specialists in applied mathematics and graduate students. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)
