We show that the Hardy-Littlewood maximal operator and a class of Calderón-Zygmund singular integrals satisfy the strong type modular inequality in variable L spaces if and only if the variable exponent p(x) ∼ const.

A systematic treatment of multilinear Calderón-Zygmund operators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, the multilinear T1 theorem, and a variety of results regarding multilinear multiplier operators.

Translation and convolution associated with discrete wavelet transform are investigated using properties of Calderón-Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain p L-spaces.

The main purpose of this paper is to establish the weighted [Formula: see text] inequalities of the oscillation and variation operators for the multilinear Calderón-Zygmund singular integral with a Lipschitz function.

We find necessary density conditions for Marcinkiewicz-Zygmund inequalities and interpolation for spaces of spherical harmonics in S with respect to the L norm. Moreover, we prove that there are no complete interpolation families for p 6= 2.

In this paper we obtain a quantitative Voronovskaja result and the exact orders in approximation by the derivatives of complex Riesz-Zygmund means in compact disks. 2000 Mathematical Subject Classification: Primary : 30E10 ; Secondary : 41A25, 41A28.

A survey of known results in the theory of convolution type Calderón-Zygmund singular integral operators with rough kernels is given. Some recent progress is discussed. A list of remaining open questions is presented.

The Fefferman-Stein vector-valued maximal function inequality is proved for spaces of homogeneous type. The approach taken here is based on the theory of vector-valued Calderón-Zygmund singular integral theory in this context, which is appropriately developed.

Let b ∈ BMO(Rn) and T be the Calderón–Zygmund singular integral operator. The commutator [b,T ] generated by b and T is defined by [b,T ] f (x) = b(x)T f (x)−T (b f )(x). By a classical result of Coifman et al [6], we know that the commutator is bounded on Lp(Rn) for 1 < p < ∞. Chanillo [1] proves a similar result when T is replaced by the fractional integral operators. In [9], the boundedness ...

We define homogeneous classes of x-dependent anisotropic symbols Ṡ γ,δ(A) in the framework determined by an expansive dilation A, thus extending the existing theory for diagonal dilations. We revisit anisotropic analogues of Hörmander-Mihlin multipliers introduced by Rivière [22] and provide direct proofs of their boundedness on Lebesgue and Hardy spaces by making use of the well-established Ca...