Multilinear Calderón-Zygmund operators on Hardy spaces.
It is shown that multilinear Calderón-Zygmund operators are bounded on products of Hardy spaces.
Multilinear Calderón-Zygmund operators on weighted Hardy spaces
Grafakos-Kalton [Collect. Math. 52 (2001)] discussed the boundedness of multilinear Calderón-Zygmund operators on the product of Hardy spaces. Then Lerner et al. [Adv. Math. 220 (2009)] defined weights and built a theory of weights adapted to multilinear Calderón-Zygmund operators. In this paper, we combine the above results and obtain some estimates for multilinear Calderón-Zygmund operators on weighted Hardy spaces and also obtain a weighted multilinear version of an inequality for multilinear...
Multilinear commutators for fractional integrals in non-homogeneous spaces.
Under the assumption that m is a non-doubling measure on Rd, the authors obtain the (Lp,Lq)-boundedness and the weak type endpoint estimate for the multilinear commutators generated by fractional integrals with RBMO (m) functions of Tolsa or with Osc exp Lr(m) functions for r greater than or equal to 1, where Osc exp Lr(m) is a space of Orlicz type satisfying that Osc exp Lr(m)=RBMO(m) if r=1 and Osc exp Lr(m) is a subset of RBMO(m) if r>1.
Multilinear Riesz potential on Morrey-Herz spaces with non-doubling measures.
Multilinear singular integral
Multilinear singular integrals.
We survey the theory of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson's operator which shows the close connection of this operator to multilinear singular integrals. We discuss particular multilinear singular integrals which historically arose in the study of eigenfunctions of Schrödinger operators.[Proceedings of the 6th International...
Multilinear singular integrals involving a derivative of fractional order
Multiparameter singular integrals and maximal functions
We prove -boundedness for a class of singular integral operators and maximal operators associated with a general -parameter family of dilations on . This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.
Multiparameter singular integrals and maximal operators along flat surfaces.
Multipliers with Singularities Along a Curve in ...
Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates
Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality of order...