CALDERÓN – ZYGMUND OPERATORS OF TYPE THETA ON A PAIR OF WEIGHTED LORENTZ SPACES

Abstract

In this paper, we study Calderón – Zygmund operators of type theta on weighted Lorentz spaces (see Definitions 1.1, 1.3 and 1.4). More precisely, we present a sufficient condition on weight functions under which the boundedness of the Calderón – Zygmund operators of type theta on a pair of weighted Lorentz spaces is established (see Theorem 3.1). Our approach is to bound the norms of such operators using the boundedness of Hardy type operators on weighted Lorentz spaces (see Lemma 2.2) and the boundedness of the Calderón – Zygmund operators of type theta on classical Lorentz spaces (see Proposition 2.3).