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.

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 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.

Marcinkiewicz integral operators on product domains

2002 ◽  
Vol 132 (3) ◽  
pp. 523-530
Author(s):  
KYUNG SOO RIM
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Cancellation Property ◽  
Product Domains ◽  
Marcinkiewicz Integral Operator

With the cancellation property of the bounded kernel, we prove that the generalized Marcinkiewicz integral operator is bounded on L2 (ℝn×ℝm) for all dimensions n, m.

scholarly journals $L^{p}$ BOUNDS FOR MARCINKIEWICZ INTEGRALS

2003 ◽  
Vol 46 (3) ◽  
pp. 669-677 ◽  
Author(s):  
Yong Ding ◽  
Yibiao Pan
Keyword(s):  
Integral Operators ◽  
Primary 42B25 ◽  
Subject Classification ◽  
Marcinkiewicz Integral ◽  
Marcinkiewicz Integrals

AbstractIn this paper the authors establish the $L^p$ boundedness for several classes of Marcinkiewicz integral operators with kernels satisfying a condition introduced by Grafakos and Stefanov in Indiana Univ. Math. J.47 (1998), 455–469.AMS 2000 Mathematics subject classification: Primary 42B25; 42B99

BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES

2015 ◽  
Vol 99 (3) ◽  
pp. 380-398 ◽  
Author(s):  
FENG LIU ◽  
SUZHEN MAO
Keyword(s):  
Radial Function ◽  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Marcinkiewicz Integrals ◽  
Parametric Marcinkiewicz Integral ◽  
Marcinkiewicz Operators ◽  
L Log L

In an extrapolation argument, we prove certain $L^{p}\,(1<p<\infty )$ estimates for nonisotropic Marcinkiewicz operators associated to surfaces under the integral kernels given by the elliptic sphere functions ${\rm\Omega}\in L(\log ^{+}L)^{{\it\alpha}}({\rm\Sigma})$ and the radial function $h\in {\mathcal{N}}_{{\it\beta}}(\mathbb{R}^{+})$. As applications, the corresponding results for parametric Marcinkiewicz integral operators related to area integrals and Littlewood–Paley $g_{{\it\lambda}}^{\ast }$-functions are given.

A CLASS OF MARCINKIEWICZ INTEGRAL OPERATORS ON PRODUCT DOMAINS

2001 ◽  
Vol 2 (3) ◽  
pp. 257 ◽  
Author(s):  
Yi-ming YING
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Product Domains

scholarly journals Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 886 ◽  
Author(s):  
Mohammed Ali ◽  
Oqlah Al-Refai
Keyword(s):  
Kernel Function ◽  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Marcinkiewicz Integrals ◽  
Block Space ◽  
Parametric Marcinkiewicz Integral

In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M Ω , ϕ , h , ρ ( r ) is considered. Under the condition that Ω is a function in L q ( S n - 1 ) with q ∈ ( 1 , 2 ] , appropriate estimates of the aforementioned operators from Triebel–Lizorkin spaces to L p spaces are obtained. By these estimates and an extrapolation argument, we establish the boundedness of such operators when the kernel function Ω belongs to the block space B q 0 , ν - 1 ( S n - 1 ) or in the space L ( l o g L ) ν ( S n - 1 ) . Our results represent improvements and extensions of some known results in generalized parametric Marcinkiewicz integrals.

scholarly journals Marcinkiewicz integral operators along twisted surfaces

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Integral Operators ◽  
Maximal Functions ◽  
Marcinkiewicz Integral ◽  
Product Domains ◽  
General Method

<p style='text-indent:20px;'>Marcinkiewicz integral operators on product domains defined by translates determined by twisted surfaces are introduced. Maximal functions along twisted surfaces are also introduced. Conditions on the underlined surfaces implying that the corresponding Marcinkiewicz integral operators map <inline-formula><tex-math id="M1">\begin{document}$ L^{p}\rightarrow L^{p} $\end{document}</tex-math></inline-formula> for <inline-formula><tex-math id="M2">\begin{document}$ 1&lt;p&lt;\infty $\end{document}</tex-math></inline-formula> are obtained. A general method involving lacunary families of multi-indices is developed.</p>

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
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