scholarly journals Norm Comparison Inequalities for the Composite Operator

2009 ◽  
Vol 2009 (1) ◽  
pp. 212915 ◽  
Author(s):  
Yuming Xing ◽  
Shusen Ding
Keyword(s):  
Composite Operator ◽  
Norm Comparison

scholarly journals Norm Comparison Estimates for the Composite Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xuexin Li ◽  
Yong Wang ◽  
Yuming Xing
Keyword(s):  
Elliptic Equation ◽  
Quasilinear Elliptic Equation ◽  
Differential Forms ◽  
Generalized Solution ◽  
Composite Operator ◽  
Potential Operator ◽  
Norm Estimates ◽  
Quasilinear Elliptic ◽  
Littlewood Maximal Operator ◽  
Norm Comparison

This paper obtains the Lipschitz and BMO norm estimates for the composite operator𝕄s∘Papplied to differential forms. Here,𝕄sis the Hardy-Littlewood maximal operator, andPis the potential operator. As applications, we obtain the norm estimates for the Jacobian subdeterminant and the generalized solution of the quasilinear elliptic equation.

WEIGHTED WEAK TYPE ENDPOINT ESTIMATES FOR THE COMPOSITIONS OF CALDERÓN–ZYGMUND OPERATORS

2019 ◽  
Vol 109 (3) ◽  
pp. 320-339 ◽  
Author(s):  
GUOEN HU
Keyword(s):  
Weak Type ◽  
Composite Operator ◽  
Weighted Estimate ◽  
Sparse Operators ◽  
Image Position

AbstractLet $T_{1}$, $T_{2}$ be two Calderón–Zygmund operators and $T_{1,b}$ be the commutator of $T_{1}$ with symbol $b\in \text{BMO}(\mathbb{R}^{n})$. In this paper, by establishing new bilinear sparse dominations and a new weighted estimate for bilinear sparse operators, we prove that the composite operator $T_{1}T_{2}$ satisfies the following estimate: for $\unicode[STIX]{x1D706}>0$ and weight $w\in A_{1}(\mathbb{R}^{n})$, $$\begin{eqnarray}\displaystyle & & \displaystyle w(\{x\in \mathbb{R}^{n}:\,|T_{1}T_{2}f(x)|>\unicode[STIX]{x1D706}\})\nonumber\\ \displaystyle & & \displaystyle \qquad \lesssim [w]_{A_{1}}[w]_{A_{\infty }}\log (\text{e}+[w]_{A_{\infty }})\int _{\mathbb{R}^{n}}\frac{|f(x)|}{\unicode[STIX]{x1D706}}\log \bigg(\text{e}+\frac{|f(x)|}{\unicode[STIX]{x1D706}}\bigg)w(x)\,dx,\nonumber\end{eqnarray}$$ while the composite operator $T_{1,b}T_{2}$ satisfies $$\begin{eqnarray}\displaystyle & & \displaystyle w(\{x\in \mathbb{R}^{n}:\,|T_{1,b}T_{2}f(x)|>\unicode[STIX]{x1D706}\})\nonumber\\ \displaystyle & & \displaystyle \qquad \lesssim [w]_{A_{1}}[w]_{A_{\infty }}^{2}\log (\text{e}+[w]_{A_{\infty }})\int _{\mathbb{R}^{n}}\frac{|f(x)|}{\unicode[STIX]{x1D706}}\log ^{2}\bigg(\text{e}+\frac{|f(x)|}{\unicode[STIX]{x1D706}}\bigg)w(x)\,dx.\nonumber\end{eqnarray}$$

scholarly journals Erratum: Composite operator and condensate in the SU(N) Yang-Mills theory with U(N−1) stability group [Phys. Rev. D 97 , 034029 (2018)]

2018 ◽  
Vol 98 (5) ◽  
Author(s):  
Matthias Warschinke ◽  
Ryutaro Matsudo ◽  
Shogo Nishino ◽  
Toru Shinohara ◽  
Kei-Ichi Kondo
Keyword(s):  
Composite Operator ◽  
Yang Mills ◽  
Stability Group

scholarly journals Composite operator and condensate in the SU(N) Yang-Mills theory with U(N−1) stability group

2018 ◽  
Vol 97 (3) ◽  
Author(s):  
Matthias Warschinke ◽  
Ryutaro Matsudo ◽  
Shogo Nishino ◽  
Toru Shinohara ◽  
Kei-Ichi Kondo
Keyword(s):  
Composite Operator ◽  
Yang Mills ◽  
Stability Group

scholarly journals Poincaré-Type Inequalities for the Composite Operator inL𝒜-Averaging Domains

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Guannan Shi ◽  
Yuming Xing ◽  
Baiqing Sun
Keyword(s):  
Maximal Operator ◽  
Poincaré Inequality ◽  
Composite Operator ◽  
Potential Operator ◽  
Poincare Inequality ◽  
Definition Of ◽  
Harmonic Equation ◽  
Poincaré Type Inequalities

We first establish the local Poincaré inequality withL𝒜-averaging domains for the composition of the sharp maximal operator and potential operator, applied to the nonhomogenousA-harmonic equation. Then, according to the definition ofL𝒜-averaging domains and relative properties, we demonstrate the global Poincaré inequality withL𝒜-averaging domains. Finally, we give some illustrations for these theorems.

scholarly journals The non-perturbative groundstate of QCD and the local composite operator A2μ

2001 ◽  
Vol 516 (3-4) ◽  
pp. 307-313 ◽  
Author(s):  
H. Verschelde ◽  
K. Knecht ◽  
K. Van Acoleyen ◽  
M. Vanderkelen
Keyword(s):  
Composite Operator
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