Triebel-Lizorkin space boundedness of Marcinkiewicz integrals associated to surfaces

2015 ◽  
Vol 30 (4) ◽  
pp. 418-446 ◽  
Author(s):  
Kôzô Yabuta
Keyword(s):  
Marcinkiewicz Integrals ◽  
Lizorkin Space

scholarly journals Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels

2020 ◽  
Vol 53 (1) ◽  
pp. 44-57
Author(s):  
Mohammed Ali ◽  
Qutaibeh Katatbeh
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Natural Extensions ◽  
Parametric Marcinkiewicz Integral ◽  
Weaker Conditions

AbstractIn this article, we study the generalized parabolic parametric Marcinkiewicz integral operators { {\mathcal M} }_{{\Omega },h,{\Phi },\lambda }^{(r)} related to polynomial compound curves. Under some weak conditions on the kernels, we establish appropriate estimates of these operators. By the virtue of the obtained estimates along with an extrapolation argument, we give the boundedness of the aforementioned operators from Triebel-Lizorkin spaces to Lp spaces under weaker conditions on Ω and h. Our results represent significant improvements and natural extensions of what was known previously.

scholarly journals Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces

2010 ◽  
Vol 62 (2) ◽  
pp. 233-262 ◽  
Author(s):  
Yong Ding ◽  
Qingying Xue ◽  
Kôzô Yabuta
Keyword(s):  
Rough Kernel ◽  
Marcinkiewicz Integrals

scholarly journals Marcinkiewicz integrals on product spaces

2005 ◽  
Vol 167 (3) ◽  
pp. 227-234 ◽  
Author(s):  
H. Al-Qassem ◽  
A. Al-Salman ◽  
L. C. Cheng ◽  
Y. Pan
Keyword(s):  
Product Spaces ◽  
Marcinkiewicz Integrals

scholarly journals A Note on Marcinkiewicz Integrals along Submanifolds of Finite Type

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Daiqing Zhang
Keyword(s):  
Finite Type ◽  
Unit Sphere ◽  
Radial Direction ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Submanifolds Of Finite Type

We study the parametric Marcinkiewicz integrals along submanifolds of finite type with rough kernels. The kernels of our operators are allowed to be very rough both on the unit sphere and in the radial direction. Under the rather weakened size conditions on the integral kernels, the Lp bounds will be established for such operators. As applications, the corresponding results for parametric Marcinkiewicz integrals related to area integrals and Littlewood-Paley gλ⁎ functions are also given.

scholarly journals Parabolic Marcinkiewicz integrals on product spaces and extrapolation

2016 ◽  
Vol 14 (1) ◽  
pp. 649-660 ◽  
Author(s):  
Mohammed Ali ◽  
Mohammed Al-Dolat
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Product Spaces ◽  
Marcinkiewicz Integrals ◽  
Product Domains

Abstract In this paper, we study the the parabolic Marcinkiewicz integral ${\cal M}_{\Omega, h}^{{\rho _{1,}}{\rho _2}}$ on product domains Rn × Rm (n, m ≥ 2). Lp estimates of such operators are obtained under weak conditions on the kernels. These estimates allow us to use an extrapolation argument to obtain some new and improved results on parabolic Marcinkiewicz integral operators.

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