• 대한수학회지
• /
• 제44권6호
• /
• pp.1255-1266
• /
• 2007

We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators $\mathcal{M}^{\rho}_{\Omega}$. As an application of this inequality, we obtain weighted $L^p$ inequalities for a class of parametric Marcinkiewicz integral operators $\mathcal{M}^{*,\rho}_{\Omega,\lambda}\;and\;\mathcal{M}^{\rho}_{\Omega,S}$ related to the Littlewood-Paley $g^*_{\lambda}-function$ and the area integral S, respectively.

• Kyungpook Mathematical Journal
• /
• 제46권1호
• /
• pp.31-48
• /
• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• 대한수학회보
• /
• 제45권1호
• /
• pp.1-10
• /
• 2008

We prove a sharp inequality for some multilinear operator related to Marcinkiewicz integral operator. As application, we obtain the weighted norm inequality and L log L type estimate for the multilinear operator.

• 대한수학회보
• /
• 제60권1호
• /
• pp.47-73
• /
• 2023

This paper is devoted to establishing certain L^p bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels given by h ∈ ∆_γ(ℝ₊) and Ω ∈ Wℱ_β(S^n-1) for some γ, β ∈ (1, ∞]. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley g^*_λ functions and area integrals are also presented.

• 대한수학회보
• /
• 제56권5호
• /
• pp.1099-1115
• /
• 2019

In the present paper, we establish certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels in Grafakos-Stefanov class ${\mathcal{F}}_{\beta}(S^{n-1})$. Our main results improve and generalize a result given by Al-Qassem, Cheng and Pan in 2012. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g^*_{\lambda}$-functions and area integrals are also presented.

• 대한수학회논문집
• /
• 제38권2호
• /
• pp.401-430
• /
• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• 대한수학회지
• /
• 제44권3호
• /
• pp.733-745
• /
• 2007

We prove the $L^p(1 boundedness of the parabolic Marcinkiewicz integral with the kernel function $\Omega{\in}L(log^+L)^{1/2}(S^{n-1})$. The result is an improvement and extension of some known results.

• Kyungpook Mathematical Journal
• /
• 제63권4호
• /
• pp.577-591
• /
• 2023

In this paper we establish the L^p boundedness of Marcinkiewicz integral operators on product domains with rough kernels satisfying a weak size condition. We assume that our kernels are supported on surfaces generated by curves more general than polynomials and convex functions. This generalizes and extends previous results.

• 대한수학회지
• /
• 제44권3호
• /
• pp.541-564
• /
• 2007

In this paper, the endpoint estimates for some multilinear operators related to certain integral operators are obtained. The operators include Littlewood-Paley operators and Marcinkiewicz operators.

• 대한수학회논문집
• /
• 제22권2호
• /
• pp.259-275
• /
• 2007

The continuity for the multilinear operators associated to some non-convolution type integral operators on Besov spaces are obtained. The operators include Littlewood-Paley operators, Marcinkiewicz operators and Bochner-Riesz operator.