A weighted vector-valued weak type (1,1) inequality and spherical summation
We prove a weighted vector-valued weak type (1,1) inequality for the Bochner-Riesz means of the critical order. In fact, we prove a slightly more general result.
Divergence of the Bochner-Riesz means in the weighted Hardy spaces
We costruct functions in () whose Fourier integral expansions are almost everywhere non-summable with respect to the Bochner-Riesz means of the critical order.
Weighted weak type (1,1) estimates for oscillatory singular integrals
We consider the -weights and prove the weighted weak type (1,1) inequalities for certain oscillatory singular integrals.
Weighted inequalities on product domains
Estimates for singular integrals and extrapolation
We study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove boundedness of the singular integrals under a certain sharp size condition on their kernels.
Boundedness of Littlewood-Paley operators relative to non-isotropic dilations
We consider Littlewood-Paley functions associated with a non-isotropic dilation group on . We prove that certain Littlewood-Paley functions defined by kernels with no regularity concerning smoothness are bounded on weighted spaces, , with weights of the Muckenhoupt class. This, in particular, generalizes a result of N. Rivière (1971).
Weighted weak type (1,1) estimates for singular integrals and Littlewood-Paley functions
We prove some weighted weak type (1,1) inequalities for certain singular integrals and Littlewood-Paley functions.
Maximal singular integrals on product homogeneous groups
We prove boundedness for p ∈ (1,∞) of maximal singular integral operators with rough kernels on product homogeneous groups under a sharp integrability condition of the kernels.
On weighted weak type norm inequalities for one-sided oscillatory singular integrals
We consider one-sided weight classes of Muckenhoupt type and study the weighted weak type (1,1) norm inequalities for a class of one-sided oscillatory singular integrals with smooth kernel.
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