Integral operators on the halfspace in generalized Lebesgue spaces Lp(·), part I

In this paper we generalize a version of the classical Calderón–Zygmund theorem on principle value integrals in generalized Lebesgue spaces Lp(·) proved in [J. Reine Angew. Math. 563 (2003) 197–220], to kernels, which do not satisfy standard estimates on Rd+1. This result will be used in part II of this paper to prove the classical theorem on halfspace estimates of Agmon, Douglis, and Nirenberg [Comm. Pure Appl. Math. 12 (1959) 623–727] for generalized Lebesgue spaces Lp(·).  2004 Elsevier Inc. All rights reserved