ترغب بنشر مسار تعليمي؟ اضغط هنا

Estimates for Schur Multipliers and Double Operator Integrals -- A Wavelet Approach

54   0   0.0 ( 0 )
 نشر من قبل Edward McDonald
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We discuss the work of Birman and Solomyak on the singular numbers of integral operators from the point of view of modern approximation theory, in particular with the use of wavelet techniques. We are able to provide a simple proof of norm estimates for integral operators with kernel in $B^{frac{1}{p}-frac{1}{2}}_{p,p}(mathbb R,L_2(mathbb R))$. This recovers, extends and sheds new light on a theorem of Birman and Solomyak. We also use these techniques to provide a simple proof of Schur multiplier bounds for double operator integrals, with bounded symbol in $B^{frac{1}{p}-frac{1}{2}}_{frac{2p}{2-p},p}(mathbb R,L_infty(mathbb R))$, which extends Birman and Solomyaks result to symbols without compact domain.



قيم البحث

اقرأ أيضاً

139 - Shuichi Sato 2010
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 con dition for the kernels. Also, we prove some weighted $L^p$ inequalities for the operators.
For $ 0< lambda < frac{1}2$, let $ B_{lambda }$ be the Bochner-Riesz multiplier of index $ lambda $ on the plane. Associated to this multiplier is the critical index $1 < p_lambda = frac{4} {3+2 lambda } < frac{4}3$. We prove a sparse bound for $ B_{ lambda }$ with indices $ (p_lambda , q)$, where $ p_lambda < q < 4$. This is a further quantification of the endpoint weak $L^{p_lambda}$ boundedness of $ B_{lambda }$, due to Seeger. Indeed, the sparse bound immediately implies new endpoint weighted weak type estimates for weights in $ A_1 cap RH_{rho }$, where $ rho > frac4 {4 - 3 p_{lambda }}$.
210 - Shuichi Sato 2008
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.
168 - Tuomas Oikari 2020
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.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا