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 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.

Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels

2015 ◽  
Vol 27 (4) ◽  
Author(s):  
Yanping Chen ◽  
Yong Ding
Keyword(s):  
Rough Kernels ◽  
Marcinkiewicz Integrals

AbstractThis paper is devoted to the study of the

scholarly journals Boundedness and Continuity of Several Integral Operators with Rough Kernels inWFβSn-1on Triebel-Lizorkin Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Feng Liu
Keyword(s):  
Besov Spaces ◽  
Singular Integrals ◽  
Integral Operators ◽  
Function Class ◽  
Function Spaces ◽  
Maximal Functions ◽  
Rough Kernels ◽  
Systematic Treatment ◽  
Marcinkiewicz Integrals

A systematic treatment is given of singular integrals and Marcinkiewicz integrals associated with surfaces generated by polynomial compound mappings as well as related maximal functions with rough kernels inWFβ(Sn-1), which relates to the Grafakos-Stefanov function class. Certain boundedness and continuity for these operators on Triebel-Lizorkin spaces and Besov spaces are proved by applying some criterions of bounds and continuity for several operators on the above function spaces.

scholarly journals Marcinkiewicz integrals along subvarieties on product domains

2004 ◽  
Vol 2004 (72) ◽  
pp. 4001-4011
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Product Domains

We study theLpmapping properties of a class of Marcinkiewicz integral operators on product domains with rough kernels supported by subvarieties.

scholarly journals The Chen-type of the noncompact cyclides of Dupin

1994 ◽  
Vol 36 (1) ◽  
pp. 71-75 ◽  
Author(s):  
Filip Defever ◽  
Ryszard Deszcz ◽  
Leopold Verstraelen
Keyword(s):  
Euclidean Space ◽  
Finite Type ◽  
Minimal Submanifolds ◽  
First Results ◽  
Finite Type Submanifolds ◽  
Submanifolds Of Finite Type

Minimal submanifolds of a Euclidean space are contained in a much larger class of submanifolds, namely in the class of submanifolds of finite type. Submanifolds of finite type were introduced about a decade ago by B. Y. Chen in [2]; the first results on this subject have been collected in the books [2], [3].

scholarly journals Rough Singular Integrals with Kernels Supported by Submanifolds of Finite Type

2005 ◽  
Vol 9 (1) ◽  
pp. 19-30 ◽  
Author(s):  
Hussain Al-Qassem ◽  
Ahmad Al-Salman ◽  
Yibiao Pan
Keyword(s):  
Finite Type ◽  
Singular Integrals ◽  
Submanifolds Of Finite Type
Sign in / Sign up

Export Citation Format

Share Document