Results 1 to 10 of about 2,906 (145)
A note on Marcinkiewicz integrals supported by submanifolds [PDF]
Journal of Inequalities and Applications, 2018 In the present paper, we establish the boundedness and continuity of the parametric Marcinkiewicz integrals with rough kernels associated to polynomial mapping P $\mathcal{P}$ as well as the corresponding compound submanifolds, which is defined by Mh,Ω ...
Feng Liu
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A Note on a Class of Generalized Parabolic Marcinkiewicz Integrals along Surfaces of Revolution [PDF]
Mathematics, 2022 In this article, certain sharp Lp estimates for a specific class of generalized Marcinkiewicz operators with mixed homogeneity associated to surfaces of revolution are established.
Mohammed Ali, Hussain Al-Qassem
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Fractional type Marcinkiewicz integral operators associated to surfaces [PDF]
, 2013 In this paper, we discuss the boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and extend a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type Marcinkiewicz
Sawano, Yoshihiro, Yabuta, Kôzô
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On an integral of Marcinkiewicz [PDF]
Transactions of the American Mathematical Society, 1959 satisfied the inequality Ap|f|lp-H / Ap ? ApIIflIp (the left side requiring, of course, that f07fdO=O). This was affirmatively answered by Zygmund in [7], to which paper the reader is referred for an account of the origin of this problem and its relation to other problems in the theory of Fourier series and in the theory of functions.
Daniel Waterman
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Marcinkiewicz integral and superdensity [PDF]
Annali di Matematica Pura ed Applicata (1923 -)Abstract In his beautiful book Singular Integrals and Differentiability Properties of Functions , E.M. Stein introduces Marcinkiewicz integral as an alternative to the differentiation theorem to illustrate (literally quoting from [1, Ch.I, Sect.2.3]) “the principle that a ...
Silvano Delladio
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Estimates for Generalized Parabolic Marcinkiewicz Integrals with Rough Kernels on Product Domains [PDF]
Axioms, 2023 We prove Lp estimates of a class of generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these estimates along with an extrapolation argument, we obtain the boundedness of our operators under very weak ...
Mohammed Ali, Hussain Al-Qassem
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Marcinkiewicz integrals on product spaces [PDF]
Studia Mathematica, 2005 Let \(d \geq 2\) (\(d = n\) or \(d=m\)) and \(S^{d-1}\) be the unit sphere in \(\mathbb R^d\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega\) is a homogeneous function of degree zero on \(\mathbb R^n\times \mathbb R\) that satisfies \(\Omega\in L(S^{n-1}\times S^{m-1})\) and \[ \int_{S^{n-1}}\Omega(x,y) d\sigma(x ...
Hussain Al-Qassem +3 more
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Fractional type Marcinkiewicz integrals over non-homogeneous metric measure spaces [PDF]
Journal of Inequalities and Applications, 2016 The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integral M β , ρ , q $\mathcal{M}_{\beta,\rho,q}$ on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling ...
Guanghui Lu, Shuangping Tao
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Boundedness of Marcinkiewicz integrals with rough kernels on Musielak-Orlicz Hardy spaces [PDF]
Journal of Inequalities and Applications, 2017 Let φ : R n × [ 0 , ∞ ) → [ 0 , ∞ ) $\varphi:\mathbb{R}^{n}\times[0, \infty) \to[0, \infty)$ satisfy that φ ( x , ⋅ ) $\varphi(x, \cdot)$ , for any given x ∈ R n $x\in\mathbb{R}^{n}$ , is an Orlicz function and φ ( ⋅ , t ) $\varphi(\cdot, t)$ is a ...
Bo Li, Minfeng Liao, Baode Li
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Integral Operators of Marcinkiewicz Type [PDF]
Journal of Integral Equations and Applications, 2002 Let \(n\geq 2\) and \(S^{n-1}\) be the unit sphere in \(\mathbb{R}^n\) equipped with the normalized Lebesgue measure \(d\sigma\). Suppose that \(\Omega\) is a homogeneous function of degree zero on \(\mathbb{R}^n\) that satisfies \(\Omega\in L(\log^+L)(S^{n-1})\) and \[ \int_{S^{n-1}} \Omega(x)\,d\sigma= 0.
Ahmad Al-Salman, Hussain Al-Qassem
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