Sharp Function Estimates Research Articles

Sharp function estimates and boundedness for Toeplitz-type operators associated with general fractional integral operators

Abstract In this paper, we establish some sharp maximal function estimates for certain Toeplitz-type operators associated with some fractional integral operators with general kernel. As an application, we obtain the boundedness of the Toeplitz-type operators on the Lebesgue, Morrey and Triebel-Lizorkin spaces. The operators include the Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

Weighted Lq(Lp)-estimate with Muckenhoupt weights for the diffusion-wave equations with time-fractional derivatives

We present a weighted Lq(Lp)-theory (p,q∈(1,∞)) with Muckenhoupt weights for the equation∂tαu(t,x)=Δu(t,x)+f(t,x),t>0,x∈Rd. Here, α∈(0,2) and ∂tα is the Caputo fractional derivative of order α. In particular we prove that for any p,q∈(1,∞), w1(x)∈Ap and w2(t)∈Aq,∫0∞(∫Rd|uxx|pw1dx)q/pw2dt≤N∫0∞(∫Rd|f|pw1dx)q/pw2dt, where Ap is the class of Muckenhoupt Ap weights. Our approach is based on the sharp function estimates of the derivatives of solutions.

Weighted Sharp function estimate and boundedness for commutator associated with singular integral operator satisfying a variant of Hörmander's condition

Weighted Sharp function estimate and boundedness for commutator associated with singular integral operator satisfying a variant of Hörmander's condition

Sharp function estimates and boundedness for commutators associated with general singular integral operator

In this paper, we establish the sharp maximal function estimates for the commutator associated with the singular integral operator with general kernel. As an application, we obtain the boundedness of the commutator on weighted Lebesgue, Morrey, and Triebel-Lizorkin spaces.

Sharp function estimates and boundedness for Toeplitz type operator related to general singular integral operator

Sharp function estimates and boundedness for Toeplitz type operator related to general singular integral operator

Weighted norm inequalities with general weights for the commutator of Calderón

In this paper, by a sharp function estimate and an idea of Lerner, the authors establish some weighted estimates for the m-multilinear integral operator which is bounded from L1(ℝn)×…×L1(ℝn) to L1/m,∞(ℝn), and the associated kernel K(x; y1, …, ym) enjoys a regularity on the variable x. As an application, weighted estimates with general weights are given for the commutator of Calderon.

Weighted estimates for the multilinear singular integral operators with non-smooth kernels

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smooth kernels.

Sharp and weighted boundedness for multilinear operators associated with pseudo-differential operators on Morrey space

The paper proves some weighted boundedness for the multilinear operators related to some pseudo-differential operators on the generalized Morrey spaces by using the sharp function estimate of the multilinear operators.

Acotaciones ponderadas para operadores integrales singulares multilineales con núcleos no suaves en espacios de Morrey

In this paper, we prove some weighted boundedness for the multilinear operators related to some singular integral operators with non-smooth kernels on the generalized Morrey spaces by using a sharp function estimate of the multilinear operators.

Weighted boundedness for multilinear singular integral operators with non-smooth kernels on Morrey spaces

In this paper, we prove some weighted boundedness for the multilinear operators related to some singular integral operators with non-smooth kernels on the generalized Morrey spaces by using a sharp function estimate of the multilinear operators.

SHARP FUNCTION ESTIMATES AND WEIGHTED NORM INEQUALITIES FOR MULTILINEAR SINGULAR INTEGRAL OPERATORS

A sharp function estimate is established for multilinear singular integral operators. As applications, some weighted norm inequalities are obtained for such operators.This research was supported by NSF of Henan Province and NNSF (No. 10271015) of China.

A sharp function estimate for multilinear singular integral operators

A variant sharp function estimate is established for the multilinear singular integral operators. Two applications of this estimate are also given.

Sharp function estimates for a class of pseudo-differential operators

Sharp function estimates for a class of pseudo-differential operators

Sharp function estimates for pseudo-differential operators of class Sρ, δm

Sharp function estimates for pseudo-differential operators of class Sρ, δm

Weighted norm inequalities for strongly singular convolution operators

We derive sharp function estimates for convolution operators whose kernels are more singular than Calderon-Zygmund kernels. This leads to weighted norm inequalities. Weighted weak ( 1 , 1 ) (1,1) results are also proved. All the results obtained are in the context of A p {A_p} weights.