ON THE REGULARIZATION OF SOME SINGULAR INTEGRAL OPERATORS. NOETHERIAN CRITERIA

Abstract

The work is centered on the study of algebra A generated by singular integral operators with shifts with continuous coefficients. Necessary and sufficient conditions are established for operators A to be Noetherian and to admit equivalent regularization in the space (,) Lp . There are constructed regularizators for Noetherian operators. The study is done in the space (, ) Lp with weight ρ(t) = t − tk n k=1 βk and is based on the theory of Ghelfand [1] concerning Banach algebras. The main results of this work were presented at the 9-th Congress of Romanian  Mathematicians, which took place in Galați, 2019.

2010 Mathematics Subject Classification: 34G10.