ENDPOINT ESTIMATES FOR MULTILINEAR INTEGRAL OPERATORS

Some BMO estimates for vector-valued multilinear singular integral operators

Let b ∈ BMO(Rn) and T be the Calderón–Zygmund singular integral operator. The commutator [b,T ] generated by b and T is defined as [b,T ]( f )(x) = b(x)T ( f )(x)−T (b f )(x). By using a classical result of Coifman et al [8], we know that the commutator [b,T ] is bounded on Lp(Rn) for 1 < p < ∞. Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. However...

Estimates of Multilinear Singular Integral Operators and Mean Oscillation

Some Estimates for Rough Multilinear Fractional Integral Operators and Rough Multi-sublinear Fractional Maximal Operators

It is well known that, for the purpose of researching non-smoothness partial differential equation, mathematicians pay more attention to the singular integrals with rough kernel. Moreover, the fractional type operators and their weighted boundedness theory play important roles in harmonic analysis and other fields, and the multilinear operators arise in numerous situations involving product-lik...

Best Constants for Certain Multilinear Integral Operators

Hilbert’s proof, apart from the determination of the best possible constant π csc(π/p), was published by Weyl [7]. The calculation of the constant, and the integral analogue of Hilbert’s double series theorem (for p = 2) are due to Schur [6]. The generalizations to other p′s of both the discrete and integral versions of this result were discovered later on by Hardy and Riesz and published by Ha...

Hardy Space Estimates for Multilinear Operators, Ii

We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue spaces Lp(Rn) into the Hardy spaces Hr(Rn). At the endpoint case r = n/n+m+ 1, where m is the highest vanishing moment of the multilinear operator, we prove a weak type result. 0. Introduction A wel...