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Weak Factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of Multilinear Riesz Transforms [PDF]
, 2016 This paper provides a constructive proof of the weak factorizations of the classical Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of ${\rm BMO}(\mathbb{R}^n)$ (the dual of $H^1(\mathbb{R}^n)$) via commutators of the multilinear Riesz transforms.
Li, Ji, Wick, Brett D.
arxiv +5 more sources
A note on precised Hardy inequalities on Carnot groups and Riemannian manifolds [PDF]
arXiv, 2010 We prove non local Hardy inequalities on Carnot groups and Riemannian manifolds, relying on integral representations of fractional Sobolev norms.
Russ, Emmanuel, Sire, Yannick
arxiv +5 more sources
Some notes on the inclusion between Morrey spaces
Journal of Mathematical Inequalities, 2022 In this paper, we show that the Morrey spaces M p q1(R n) cannot be contained in the weak Morrey spaces wM p q2 (R n) for q1 = q2 . We also show that the vanishing Morrey spaces V M p q(R n) are not empty and properly contained in the Morrey spaces M p q
Philotheus E. A. Tuerah, N. Tumalun
semanticscholar +1 more source
Journal of Mathematical Inequalities, 2022 Let G = ( RN ,◦,δλ ) be a homogeneous group, Q be the homogeneous dimension of G , X0,X1, . . . ,Xm be left invariant real vector fields on G and satisfy Hörmander’s rank condition on RN . Assume that X1, . . . ,Xm (m N − 1) are homogeneous of degree one
V. Guliyev
semanticscholar +1 more source
Two type Estimates for the Boundedness of Generalized Riesz Potential Operator in the Generalized Weighted Local Morrey Spaces [PDF]
, 2021 In this paper, we prove the Spanne-type boundedness of the generalized Riesz potential operator Iρ from the one generalized weighted local Morrey spaces M {x0} p,φ1 (w p,Rn) to the another one M {x0} q,φ2 (w q,Rn) with wq ∈ A1+ q p′ for 1 < p < q < ∞ and
A. Kucukaslan
semanticscholar +1 more source
Open Mathematics, 2021 This paper is devoted to the weak and strong estimates for the linear and multilinear fractional Hausdorff operators on the Heisenberg group Hn{{\mathbb{H}}}^{n}. A sharp strong estimate for TΦm{T}_{\Phi }^{m} is obtained.
Deng Yangkendi +3 more
doaj +1 more source
Multilinear Hausdorff operator and commutators on weighted Morrey and Herz spaces
Operators and Matrices, 2021 In this paper, we establish some necessary and sufficient conditions for the boundedness of multilinear Hausdorff operators on weighted central Morrey and Herz type spaces.
D. Duong, N. T. Hong
semanticscholar +1 more source
Estimates for certain class of rough generalized Marcinkiewicz functions along submanifolds
Open Mathematics, 2023 We establish certain delicate Lp{L}^{p} bounds for a class of generalized Marcinkiewicz integral operators along submanifolds with rough kernels.
Ali Mohammed, Al-Qassem Hussain
doaj +1 more source
Weighted W1, p (·)-Regularity for Degenerate Elliptic Equations in Reifenberg Domains
Advances in Nonlinear Analysis, 2021 Let w be a Muckenhoupt A2(ℝn) weight and Ω a bounded Reifenberg flat domain in ℝn. Assume that p (·):Ω → (1, ∞) is a variable exponent satisfying the log-Hölder continuous condition.
Zhang Junqiang, Yang Dachun, Yang Sibei
doaj +1 more source
Regularity properties of Haar Frames
Comptes rendus. Mathematique, 2021 We prove that pointwise and global Hölder regularity can be characterized using the coefficients on the Haar tight frame obtained by using a finite union of shifted Haar bases, despite the fact that the elements composing the frame are discontinuous ...
Stéphane Jaffard, Hamid Krim
semanticscholar +1 more source