scholarly journals Weak type $(1,1)$ estimates for Marcinkiewicz integrals with rough kernels

2001 ◽  
Vol 53 (2) ◽  
pp. 265-284 ◽  
Author(s):  
Dashan Fan ◽  
Shuichi Sato
Keyword(s):  
Weak Type ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals

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 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.

Weighted inequalities for some integral operators with rough kernels

2014 ◽  
Vol 12 (4) ◽  
Author(s):  
María Riveros ◽  
Marta Urciuolo
Keyword(s):  
Weak Type ◽  
Integral Operators ◽  
Degree Zero ◽  
Weighted Inequalities ◽  
Rough Kernels ◽  
Type Estimate ◽  
Dini Condition ◽  
Weighted Bmo ◽  
Weak Type Estimates ◽  
Invertible Matrices

AbstractIn this paper we study integral operators with kernels $$K(x,y) = k_1 (x - A_1 y) \cdots k_m \left( {x - A_m y} \right),$$ $$k_i \left( x \right) = {{\Omega _i \left( x \right)} \mathord{\left/ {\vphantom {{\Omega _i \left( x \right)} {\left| x \right|}}} \right. \kern-\nulldelimiterspace} {\left| x \right|}}^{{n \mathord{\left/ {\vphantom {n {q_i }}} \right. \kern-\nulldelimiterspace} {q_i }}}$$ where Ωi: ℝn → ℝ are homogeneous functions of degree zero, satisfying a size and a Dini condition, A i are certain invertible matrices, and n/q 1 +…+n/q m = n−α, 0 ≤ α < n. We obtain the appropriate weighted L p-L q estimate, the weighted BMO and weak type estimates for certain weights in A(p, q). We also give a Coifman type estimate for these operators.

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.

Weak type L1 boundedness of CZOs with odd rough kernels

2019 ◽  
Vol 479 (1) ◽  
pp. 855-871
Author(s):  
Qiang Huang ◽  
Zheng Wang
Keyword(s):  
Weak Type ◽  
Rough Kernels
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