Search

In this paper we generalize, under slightly more restrictive conditions on the kernel K, the classical theorem on halfspace estimates of Agmon, Douglis and Nirenberg [Comm. Pure Appl. Math. 12 (1959) 623–727] to generalized Lebesgue spaces . In particular this yields -estimates in for the Laplace equation and the Stokes system. [Copyright &y& Elsevier]

In this paper we generalize a version of the classical Calderón–Zygmund theorem on principle value integrals in generalized Lebesgue spaces proved in [J. Reine Angew. Math. 563 (2003) 197–220], to kernels, which do not satisfy standard estimates on . 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 . [Copyright &y& Elsevier]