scholarly journals Generalized Parabolic Marcinkiewicz Integral Operators Related to Surfaces of Revolution

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1200
Author(s):  
Amer Darweesh ◽  
Mohammed Ali
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Surfaces Of Revolution ◽  
Parametric Marcinkiewicz Integral

In this work, the generalized parametric Marcinkiewicz integral operators with mixed homogeneity related to surfaces of revolution are studied. Under some weak conditions on the kernels, the boundedness of such operators from Triebel–Lizorkin spaces to L p spaces are established. Our results, with the help of an extrapolation argument, improve and extend some previous known results.

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.

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.

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 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 Lp estimates for maximal functions along surfaces of revolution on product spaces

2019 ◽  
Vol 17 (1) ◽  
pp. 1361-1373 ◽  
Author(s):  
Mohammed Ali ◽  
Musa Reyyashi
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Product Spaces ◽  
Surfaces Of Revolution ◽  
Lp Estimates ◽  
Block Space

Abstract This paper is concerned with establishing Lp estimates for a class of maximal operators associated to surfaces of revolution with kernels in Lq(Sn−1 × Sm−1), q > 1. These estimates are used in extrapolation to obtain the Lp boundedness of the maximal operators and the related singular integral operators when their kernels are in the L(logL)κ(Sn−1 × Sm−1) or in the block space $\begin{array}{} B^{0,\kappa-1}_ q \end{array}$(Sn−1 × Sm−1). Our results substantially improve and extend some known results.

Fractional type Marcinkiewicz integral operators on function spaces

2015 ◽  
Vol 27 (5) ◽  
Author(s):  
Qingying Xue ◽  
Kôzô Yabuta ◽  
Jingquan Yan
Keyword(s):  
Integral Operators ◽  
Function Spaces ◽  
Marcinkiewicz Integral ◽  
Fractional Type

AbstractIn this paper, we discussed about the boundedness of the fractional type Marcinkiewicz integral operators, and improved a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel–Lizorkin spaces

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 Morrey Spaces for Nonhomogeneous Metric Measure Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Cao Yonghui ◽  
Zhou Jiang
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Marcinkiewicz Integral ◽  
Metric Measure Spaces ◽  
Measure Spaces ◽  
Definition Of

The authors give a definition of Morrey spaces for nonhomogeneous metric measure spaces and investigate the boundedness of some classical operators including maximal operator, fractional integral operator, and Marcinkiewicz integral operators.

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