$$L^p$$ L p -Estimates for Singular Oscillatory Integral Operators

Lp Estimates for Marcinkiewicz integral operators and extrapolation

*Correspondence: [email protected] Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan Abstract In this article, we establish Lp estimates for parametric Marcinkiewicz integral operators with rough kernels. These estimates and extrapolation arguments improve and extend some known results on Marcinkiewicz integrals. MSC: Primary 40B20; secondary 4...

operators on L ( L p ) and ` p - strictly singular operators

A classification of weakly compact multiplication operators on L(Lp), 1 < p < ∞, is given. This answers a question raised by Saksman and Tylli in 1992. The classification involves the concept of `p-strictly singular operators, and we also investigate the structure of general `p-strictly singular operators on Lp . The main result is that if an operator T on Lp , 1 < p < 2, is `p-strictly singula...

Damping Estimates for Oscillatory Integral Operators with Finite Type Singularities

We derive damping estimates and asymptotics of L operator norms for oscillatory integral operators with finite type singularities. The methods are based on incorporating finite type conditions into L almost orthogonality technique of Cotlar-Stein.

Damping Estimates for Oscillatory Integral Operators with Finite Type Singularities

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...