scholarly journals Commutators with Lipschitz Functions and Nonintegral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Peizhu Xie ◽  
Ruming Gong
Keyword(s):  
Integral Representation ◽  
Fractional Power ◽  
Divergence Form ◽  
Elliptic Operators ◽  
Second Order ◽  
Lipschitz Functions ◽  
Positive Operators ◽  
Riesz Transforms ◽  
Spectral Multipliers ◽  
Size Estimates

LetTbe a singular nonintegral operator; that is, it does not have an integral representation by a kernel with size estimates, even rough. In this paper, we consider the boundedness of commutators withTand Lipschitz functions. Applications include spectral multipliers of self-adjoint, positive operators, Riesz transforms of second-order divergence form operators, and fractional power of elliptic operators.

scholarly journals Boundary rectifiability and elliptic operators with W 1,1 coefficients

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Tatiana Toro ◽  
Zihui Zhao
Keyword(s):  
Divergence Form ◽  
Elliptic Operators ◽  
Second Order

AbstractWe consider second-order divergence form elliptic operators with

scholarly journals Commutators of Square Functions Related to Fractional Differentiation for Second-Order Elliptic Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Xiongtao Wu ◽  
Wenyu Tao ◽  
Yanping Chen ◽  
Kai Zhu
Keyword(s):  
Elliptic Operator ◽  
Divergence Form ◽  
Elliptic Operators ◽  
Second Order ◽  
Square Function ◽  
Fractional Differentiation ◽  
Square Functions ◽  
Second Order Elliptic Operators ◽  
Complex Coefficients

Let L=-div(A∇) be a second-order divergence form elliptic operator, where A is an accretive n×n matrix with bounded measurable complex coefficients in Rn. In this paper, we mainly establish the Lp boundedness for the commutators generated by b∈Iα(BMO) and the square function related to fractional differentiation for second-order elliptic operators.

ON SECOND-ORDER ALMOST-PERIODIC ELLIPTIC OPERATORS

2001 ◽  
Vol 63 (3) ◽  
pp. 735-753 ◽  
Author(s):  
N. DUNGEY ◽  
A. F. M. TER ELST ◽  
DEREK W. ROBINSON
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Behaviour ◽  
Large Time ◽  
Divergence Form ◽  
Elliptic Operators ◽  
Second Order ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Hölder Continuous ◽  
Leading Term

The paper considers second-order, strongly elliptic, operators H with complex almost-periodic coefficients in divergence form on Rd. First, it is proved that the corresponding heat kernel is Hölder continuous and Gaussian bounds are derived with the correct small and large time asymptotic behaviour on the kernel and its Hölder derivatives. Secondly, it is established that the kernel has a variety of properties of almost-periodicity. Thirdly, it is demonstrated that the kernel of the homogenization Ĥ of H is the leading term in the asymptotic expansion of t [map ] Kt.

On second-order periodic elliptic operators in divergence form

2001 ◽  
Vol 238 (3) ◽  
pp. 569-637 ◽  
Author(s):  
A.F.M. ter Elst ◽  
Derek W. Robinson ◽  
Adam Sikora
Keyword(s):  
Divergence Form ◽  
Elliptic Operators ◽  
Second Order
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