Results 111 to 120 of about 201 (131)

A note on the generalized Marcinkiewicz integral operators with rough kernels

Acta Mathematica Sinica, English Series, 2012
The authors study the generalized Marcinkiewicz integral operators \(M_{\Omega,r}\) on the product space \({\mathbb R}^n\times{\mathbb R}^m\). Under the condition that \(\Omega\) is a function in certain block spaces, which is optimal in some senses, the boundedness of such operators from Triebel-Lizorkin spaces to \(L^p\) spaces is obtained.
Huo Xiong Wu
exaly   +3 more sources

Boundedness of generalized marcinkiewicz integral on the Hp-sobolev spaces

Applied Mathematics, 2004
Let \(\mathbb{R}^n,\) \(n\) \(\geq 2\) be the \(n\)-dimensional Euclidean space and \( \mathbb{S}^{n-1}\) be the unit sphere in \(\mathbb{R}^n\) equipped with the normalized Lebesgue measure \(d\sigma \). The authors of this paper study the following generalized Marcinkiewicz integral operator \[ \mu _{\Omega ,\alpha }f(x)=\left(\int\nolimits_0^\infty \
Liya Jiang, Houyu Jia
exaly   +2 more sources

Generalized Marcinkiewicz Laws for Weighted Dependent Random Vectors in Hilbert Spaces

Theory of Probability & Its Applications, 2022
Целью статьи является применение теории правильно меняющихся функций для изучения слабого и усиленного законов больших чисел Марцинкевича для взвешенных сумм $S_n=\sum_{j=1}^{m_n}c_{nj}X_j$, где $\{X_n, n\geq 1\}$ - последовательность зависимых случайных векторов в гильбертовом пространстве и $(c_{nj})$ - вещественные числа.
Son, T. C., Dung, L. V., Dat, D. T., Trang, T. T.   +3 more
openaire   +2 more sources

Generalized Parabolic Marcinkiewicz Integral Operators Related to Surfaces of Revolution [PDF]

Mathematics, 2019
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.
Amer Darweesh, Mohammed Ali
exaly   +2 more sources

On the Generalized Marcinkiewicz Integral Operators with Rough Kernels

Canadian Mathematical Bulletin, 2011
AbstractA class of generalized Marcinkiewicz integral operators is introduced, and, under rather weak conditions on the integral kernels, the boundedness of such operators on Lp and Triebel–Lizorkin spaces is established.
Fan, Dashan, Wu, Huoxiong
openaire   +2 more sources

A generalized Marcinkiewicz interpolation theorem and its applications

Wuhan University Journal of Natural Sciences, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Peide, Wei, Wenzhan
openaire   +2 more sources

Weighted Lp Estimates for Multiple Generalized Marcinkiewicz Functions

Symmetry
In this paper we investigate the weighted Lp boundedness of generalized Marcinkiewicz integrals MK(ε) over multiple symmetric domains. Under the conditions K∈Lq(Sm−1×Sn−1), q>1, we establish suitable weighted Lp bounds for the integrals MK(ε). These bounds are combined with Yano’s extrapolation argument to obtain the weighted Lp boundedness of MK(ε)
Hussain Al-Qassem, Mohammed Ali
exaly   +2 more sources

Generalization of a theorem of Marcinkiewicz-Zygmund

Mathematical Notes, 1995
Let \(T_n(x)\) be a trigonometric polynomial of order at most \(n\). For the case \(0< p< 1\), the partition \(R= \{z_i\}^\ell_{i= 1}\) \((\ell= \ell(p, n))\) of the segment \([0, 2\pi)\) is found, under which the equivalence of the discrete norm \(|T_n|_{p, R}= \{{1\over \ell} \sum^\ell_{i= 1} |T_n(z_i)|^p\}^{1/p}\) and of the continuous norm \(|T_n ...
openaire   +1 more source

Generalized commutators for Marcinkiewicz type integrals with variable kernels

Acta Mathematicae Applicatae Sinica, English Series, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mo, Hui-Xia, Lu, Shan-Zhen
openaire   +1 more source

Boundedness of the parametric Marcinkiewicz integral operator and its commutators on generalized Morrey spaces

Georgian Mathematical Journal, 2012
The authors study the boundedness of the parametric Marcinkiewicz operator on generalized Morrey spaces. They find sufficient conditions to ensure the boundedness of the operator. As an application, they obtain the boundedness of a commutator of Marcinkiewicz operators on Morrey spaces.
Aliev, Seymur S., Guliev, Vagif S.
exaly   +4 more sources