Harmonic Functions, Conjugate Harmonic Functions and the Hardy Space $$H^1$$H1 in the Rational Dunkl Setting [PDF]
Journal of Fourier Analysis and Applications, 2018 In this work we extend the theory of the classical Hardy space $$H^1$$H1 to the rational Dunkl setting. Specifically, let $$\Delta $$Δ be the Dunkl Laplacian on a Euclidean space $$\mathbb {R}^N$$RN. On the half-space $$\mathbb {R}_+\times \mathbb {R}^N$$
Jean-Philippe Anker +2 more
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Quasiconvexity, Null Lagrangians, and Hardy Space Integrability Under Constant Rank Constraints [PDF]
Archive for Rational Mechanics and Analysis, 2019 We present a systematic treatment of the theory of Compensated Compactness under Murat’s constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result for signed integrands, extending aspects of the results of Fonseca–Müller.
André Guerra, Bogdan Raiță
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The periodic dilation completeness problem: cyclic vectors in the Hardy space over the infinite‐dimensional polydisk [PDF]
Journal of the London Mathematical Society, 2019 The classical completeness problem raised by Beurling and independently by Wintner asks for which ψ∈L2(0,1) , the dilation system {ψ(kx):k=1,2,…} is complete in L2(0,1) , where ψ is identified with its extension to an odd 2‐periodic function on R .
H. Dan, K. Guo
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Remark on atomic decompositions for the Hardy space $H^1$ in the rational Dunkl setting [PDF]
Studia Mathematica, 2018 Let $\Delta$ be the Dunkl Laplacian on $\mathbb R^N$ associated with a normalized root system $R$ and a multiplicity function $k(\alpha)\geq 0$. We say that a function $f$ belongs to the Hardy space $H^1_{\Delta}$ if the nontangential maximal function ...
Jacek Dziuba'nski, Agnieszka Hejna
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Composition–differentiation operators on the Hardy space
Proceedings of the American Mathematical Society, 2020 Let φ \varphi be a nonconstant analytic self-map of the open unit disk in C \mathbb {C} , with ‖ φ ‖ ∞ > 1 ...
M. Fatehi, Christopher N. B. Hammond
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Weak Factorizations of the Hardy Space H 1(ℝ n ) in Terms of Multilinear Riesz Transforms [PDF]
Canadian mathematical bulletin, 2016 This paper provides a constructive proof of the weak factorization of the classical Hardy space ${{H}^{1}}({{\mathbb{R}}^{n}})$ in terms of multilinear Riesz transforms.
Ji Li, B. Wick
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Volterra integration operators from Hardy-type tent spaces to Hardy spaces
Journal of Inequalities and Applications, 2022 In this paper, we completely characterize the boundedness and compactness of the Volterra integration operators J g $J_{g}$ acting from the Hardy-type tent spaces HT q , α p ( B n ) to the Hardy spaces H t ( B n ) in the unit ball of C n for all 0 < p ...
Rong Hu, Chuan Qin, Lv Zhou
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Column extreme multipliers of the Free Hardy Space [PDF]
Journal of the London Mathematical Society, 2018 The full Fock space over Cd can be identified with the Free Hardy Space, H2(BNd) — the unique non‐commutative reproducing kernel Hilbert space corresponding to a non‐commutative Szegö kernel on the non‐commutative, multi‐variable open unit ball BNd:=⨆n=1∞
M. Jury, R.T.W. Martin
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Orthorecursive expansions generated by the Szego kernel [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2023 This article considers systems of subspaces of the Hardy space generated by the Szego kernel. The main result of the work is to establish the convergence of orthorecursive expansions with respect to the considered systems of subspaces.
Terekhin, Pavel A.
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L p $L^{p}$ Hardy type inequality in the half-space on the H-type group
Journal of Inequalities and Applications, 2016 In the current work we studied Hardy type and L p $L^{p}$ Hardy type inequalities in the half-space on the H-type group, where the Hardy inequality in the upper half-space R + n $\mathbf{R}_{+}^{n}$ was proved by Tidblom in (J. Funct. Anal.
Jianxun He, Mingkai Yin
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