Symbols of parabolic singular integrals

1967 ◽  
pp. 184-195
Author(s):  
M. Jodeit
Keyword(s):  
Singular Integrals ◽  
Parabolic Singular Integrals

scholarly journals Weak-type (1, 1) estimates for parabolic singular integrals

2011 ◽  
Vol 54 (1) ◽  
pp. 221-247 ◽  
Author(s):  
Shuichi Sato
Keyword(s):  
Singular Integrals ◽  
Weak Type ◽  
Parabolic Singular Integrals

AbstractWe prove weak-type (1, 1) estimates for rough parabolic singular integrals on ℝ2 under the L log L condition on their kernels.

scholarly journals A charaterization of commutators for parabolic singular integrals

2011 ◽  
Vol 108 (1) ◽  
pp. 5
Author(s):  
Yanping Chen ◽  
Yong Ding
Keyword(s):  
Orlicz Space ◽  
Kernel Function ◽  
Unit Sphere ◽  
Singular Integrals ◽  
Bounded Operator ◽  
Parabolic Singular Integrals

In this paper, the authors give a characterization of the $L^p$-boundedness of the commutators for the parabolic singular integrals. More precisely, the authors prove that if $b\in \mathrm{BMO}_\varphi(\mathsf{R}^n,\rho)$, then the commutator $[b,T]$ is a bounded operator from $L^p(\mathsf{R}^n)$ to the Orlicz space $L_\psi(\mathsf{R}^n)$, where the kernel function $\Omega$ has no any smoothness on the unit sphere $S^{n-1}$. Conversely, if assuming on $\Omega$ a slight smoothness on $S^{n-1}$, then the boundedness of $[b,T]$ from $L^p(\mathsf{R}^n)$ to $L_\psi(\mathsf{R}^n)$ implies that $b\in \mathrm{BMO}_\varphi(\mathsf{R}^n,\rho)$. The results in this paper improve essentially and extend some known conclusions.

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