اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEstimates for singular integrals on homogeneous groups
92
0
0.0
(
0
)
تأليف
Shuichi Sato
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a sharp condition for the kernels. Also, we prove some weighted $L^p$ inequalities for the operators.
قيم البحث
اقرأ أيضاً
We prove certain $L^p$ estimates ($1<p<infty$) for non-isotropic singular integrals along surfaces of revolution. As an application we obtain $L^p$ boundedness of the singular integrals under a sharp size condition on their kernels.
The purpose of this paper is to establish some one-sided estimates for oscillatory singular integrals. The boundedness of certain oscillatory singular integral on weighted Hardy spaces $H^{1}_{+}(w)$ is proved. It is here also show that the $H^{1}_{+
}(w)$ theory of oscillatory singular integrals above cannot be extended to the case of $H^{q}_{+}(w)$ when $0<q<1$ and $win A_{p}^{+}$, a wider weight class than the classical Muckenhoupt class. Furthermore, a criterion on the weighted $L^{p}$-boundednesss of the oscillatory singular integral is given.
We study the commutators $[b,T]$ of pointwise multiplications and bi-parameter Calderon-Zygmund operators and characterize their off-diagonal $L^{p_1}L^{p_2} to L^{q_1}L^{q_2}$ boundedness in the range $(1,infty)$ for several of the mixed norm integrability exponents.
In this paper, we are interested in the following bilinear fractional integral operator $Bmathcal{I}_alpha$ defined by [ Bmathcal{I}_{alpha}({f,g})(x)=int_{% %TCIMACRO{U{211d} }% %BeginExpansion mathbb{R} %EndExpansion ^{n}}frac{f(x-y)g(x+y)}{|y|^{
n-alpha}}dy, ] with $0< alpha<n$. We prove the weighted boundedness of $Bmathcal{I}_alpha$ on the Morrey type spaces. Moreover, an Olsen type inequality for $Bmathcal{I}_alpha$ is also given.
We establish $L^2$ boundedness of all nice parabolic singular integrals on Good Parabolic Graphs, aka {em regular} Lip(1,1/2) graphs. The novelty here is that we include non-homogeneous kernels, which are relevant to the theory of parabolic uniform r
ectifiability. Previously, the third named author had treated the case of homogeneous kernels. The present proof combines the methods of that work (which in turn was based on methods described in Christs CBMS lecture notes), with the techniques of Coifman-David-Meyer. This is a very preliminary draft. Eventually, these results will be part of a more extensive work on parabolic uniform rectifiability and singular integrals.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
