We present a framework that yields a variety of weighted and vector-valued estimates for maximally modulated Calderón-Zygmund singular (and maximal singular) integrals from a single a priori weak type unweighted estimate for the maximal modulations of such operators. We discuss two approaches, one based on the good-λ method of Coifman and Fefferman [CF] and an alternative method employing the s...

Let T be the Calderón-Zygmund singular integral operator, a well-known result of Coifman et al. (see [6]) states that the commutator [b,T]( f ) = T(b f )− bT( f ) (where b ∈ BMO) is bounded on Lp(Rn) (1 < p <∞); Chanillo (see [1]) proves a similar result when T is replaced by the fractional integral operator; in [8, 9], these results on the TriebelLizorkin spaces and the case b ∈ Lipβ (where Li...

We give different types of new characterizations for the boundedness and essential norms generalized weighted composition operators between Zygmund-type spaces. Consequently, we obtain compactness such operators.

Abstract We study the so-called John–Nirenberg space that is a generalization of functions bounded mean oscillation in setting metric measure spaces with doubling measure. Our main results are local and global inequalities, which give weak-type estimates for function. consider medians instead integral averages throughout, thus not priori assumed to be locally integrable. arguments based on Cald...

Abstract We present a transplantation theorem for Laguerre coefficients in weighted spaces by means of discrete local Calderón–Zygmund theory.

We prove that the existence of an accretive system in the sense of M. Christ is equivalent to the boundedness of a Calderón-Zygmund operator on L2(μ). We do not assume any kind of doubling condition on the measure μ, so we are in the nonhomogeneous situation. Another interesting difference from the theorem of Christ is that we allow the operator to send the functions of our accretive system int...