Results 41 to 50 of about 85 (84)

Rough Marcinkiewicz integral operators

International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 8, Page 495-503, 2001., 2001
We study the Marcinkiewicz integral operator M𝒫f(x)=(∫−∞∞|∫|y|≤2tf(x−𝒫(y))(Ω(y)/|y|n−1)dy|2dt/22t)12/, where 𝒫 is a polynomial mapping from ℝn into ℝd and Ω is a homogeneous function of degree zero on ℝn with mean value zero over the unit sphere Sn−1. We prove an Lp boundedness result of M𝒫 for rough Ω.
Hussain Al-Qassem, Ahmad Al-Salman
wiley   +1 more source

A commutator theorem for fractional integrals in spaces of homogeneous type

International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 6, Page 403-418, 2000., 2000
We give a new proof of a commutator theorem for fractional integrals in spaces of homogeneous type.
Jorge J. Betancor
wiley   +1 more source

Sharp smoothing properties of averages over curves

Forum of Mathematics, Pi, 2023
We prove sharp smoothing properties of the averaging operator defined by convolution with a measure on a smooth nondegenerate curve $\gamma $ in $\mathbb R^d$ , $d\ge 3$ .
Hyerim Ko, Sanghyuk Lee, Sewook Oh
doaj   +1 more source

Estimates for bilinear θ-type generalized fractional integral and its commutator on new non-homogeneous generalized Morrey spaces

Analysis and Geometry in Metric Spaces, 2023
Let (X,d,μ)\left({\mathcal{X}},d,\mu ) be a non-homogeneous metric measure space satisfying the geometrically doubling and upper doubling conditions. In this setting, we first introduce a generalized Morrey space Mpu(μ){M}_{p}^{u}\left(\mu ), where 1 ...
Lu Guanghui, Wang Miaomiao, Tao Shuangping   +2 more
doaj   +1 more source

Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates

Forum of Mathematics, Sigma, 2021
We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein–Gordon and fractional Schrödinger equations.
Neal Bez, Sanghyuk Lee, Shohei Nakamura
doaj   +1 more source

Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications

Open Mathematics, 2023
In this article, we introduce anisotropic mixed-norm Herz spaces K˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}) and Kq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb ...
Zhao Yichun, Zhou Jiang
doaj   +1 more source

Global boundedness of a class of multilinear Fourier integral operators

Forum of Mathematics, Sigma, 2021
We establish the global regularity of multilinear Fourier integral operators that are associated to nonlinear wave equations on products of $L^p$ spaces by proving endpoint boundedness on suitable product spaces containing combinations of the local ...
Salvador Rodríguez-López, David Rule, Wolfgang Staubach   +2 more
doaj   +1 more source

Construction of Frames on the Heisenberg Groups

Analysis and Geometry in Metric Spaces, 2020
In this paper, we present a construction of frames on the Heisenberg group without using the Fourier transform. Our methods are based on the Calderón-Zygmund operator theory and Coifman’s decomposition of the identity operator on the Heisenberg group ...
Chang Der-Chen, Han Yongsheng, Wu Xinfeng   +2 more
doaj   +1 more source

Estimates for evolutionary partial differential equations in classical function spaces

Forum of Mathematics, Sigma, 2023
We establish new local and global estimates for evolutionary partial differential equations in classical Banach and quasi-Banach spaces that appear most frequently in the theory of partial differential equations.
Alejandro J. Castro, Anders Israelsson, Wolfgang Staubach, Madi Yerlanov   +3 more
doaj   +1 more source

On certain trilinear oscillatory integral inequalities

Advanced Nonlinear Studies
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms of Lebesgue ...
Christ Michael
doaj   +1 more source