Memoirs of the American Mathematical Society 1995; 157 pp; softcover Volume: 114 ISBN10: 0821803603 ISBN13: 9780821803608 List Price: US$44 Individual Members: US$26.40 Institutional Members: US$35.20 Order Code: MEMO/114/545
 Recent years have seen renewed interest in the solution of parabolic boundary value problems by the method of layer potentials, a method that has been extraordinarily useful in the solution of elliptic problems. This book develops this method for the heat equation in timevarying domains. In the first chapter, Lewis and Murray show that certain singular integral operators on \(L^p\) are bounded. In the second chapter, they develop a modification of the David buildup scheme, as well as some extension theorems, to obtain \(L^p\) boundedness of the double layer heat potential on the boundary of the domains. The third chapter uses the results of the first two, along with a buildup scheme, to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure. Lewis and Murray also obtain \(A_\infty\) results and discuss the Dirichlet and Neumann problems for a certain subclass of the domains. Readership Researchers and graduate students studying harmonic analysis and partial differential equations. Table of Contents  Singular integrals
 The David buildup scheme
 Absolute continuity and DirichletNeumann problems
