Corrigendum to: An extension problem and trace Hardy inequality for the sublaplacian on H-type groups

2021 ◽  
Author(s):  
Luz Roncal ◽  
Sundaram Thangavelu
Keyword(s):  
Hardy Inequality ◽  
Extension Problem

Abstract Recently we have found a couple of errors in our paper entitled An extension problem and trace Hardy inequality for the sub-Laplacian on $H$-type groups, Int. Math. Res. Not. IMRN (2020), no. 14, 4238–4294. They concern Propositions 3.12–3.13, and Theorem 1.5, Corollary 1.6 and Remark 4.10. The purpose of this corrigendum is to point out the errors and supply necessary modifications where it is applicable.

scholarly journals An Extension Problem and Trace Hardy Inequality for the Sub-Laplacian on H-type Groups

2018 ◽  
Vol 2020 (14) ◽  
pp. 4238-4294 ◽  
Author(s):  
Luz Roncal ◽  
Sundaram Thangavelu
Keyword(s):  
Hardy Inequality ◽  
Extension Problem ◽  
Fractional Powers ◽  
Hardy Inequalities ◽  
Type Group

Abstract In this paper we study the extension problem for the sub-Laplacian on an $H$-type group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sub-Laplacian.

scholarly journals Heat kernels of the discrete Laguerre operators

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
Aleksey Kostenko
Keyword(s):  
Hardy Inequality ◽  
Jacobi Polynomials ◽  
Heat Kernels ◽  
The Other ◽  
Heat Semigroup ◽  
Stochastic Completeness ◽  
Markovian Semigroup ◽  
Other Hand ◽  
The One

AbstractFor the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This enables us to show that the heat semigroup is ultracontractive and to compute the corresponding norms. On the one hand, this helps us to answer basic questions (recurrence, stochastic completeness) regarding the associated Markovian semigroup. On the other hand, we prove the analogs of the Cwiekel–Lieb–Rosenblum and the Bargmann estimates for perturbations of the Laguerre operators, as well as the optimal Hardy inequality.

scholarly journals On Negligible and Absolutely Nonmeasurable Subsets of the Euclidean Plane

2004 ◽  
Vol 11 (3) ◽  
pp. 479-487
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Plane ◽  
Identity Transformation ◽  
Extension Problem ◽  
Measure Extension ◽  
Nonmeasurable Set

Abstract The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑2 which are 𝑇2-negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇2 denotes the group of all translations of 𝐑2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇2, where 𝑔 is an arbitrary rotation of 𝐑2 distinct from the identity transformation and all central symmetries of 𝐑2.

On the isometric extension problem

2013 ◽  
Vol 36 (3) ◽  
pp. 321-330
Author(s):  
Ruidong Wang
Keyword(s):  
Extension Problem ◽  
Isometric Extension

On the End Extension Problem For Δ0-PA(S)

1989 ◽  
Vol 35 (5) ◽  
pp. 391-397
Author(s):  
Henryk Kotlarski
Keyword(s):  
Extension Problem

MAZUR–ULAM PROPERTY OF THE SUM OF TWO STRICTLY CONVEX BANACH SPACES

2015 ◽  
Vol 93 (3) ◽  
pp. 473-485 ◽  
Author(s):  
JIAN-ZE LI
Keyword(s):  
Banach Spaces ◽  
Equivalent Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Extension Problem ◽  
Isometric Extension ◽  
Strictly Convex ◽  
Necessary And Sufficient ◽  
Strictly Convex Banach Spaces ◽  
Equivalent Conditions

In this article, we study the Mazur–Ulam property of the sum of two strictly convex Banach spaces. We give an equivalent form of the isometric extension problem and two equivalent conditions to decide whether all strictly convex Banach spaces admit the Mazur–Ulam property. We also find necessary and sufficient conditions under which the $\ell ^{1}$-sum and the $\ell ^{\infty }$-sum of two strictly convex Banach spaces admit the Mazur–Ulam property.

scholarly journals Algorithmic Solvability of the Lifting-Extension Problem

2017 ◽  
Vol 57 (4) ◽  
pp. 915-965 ◽  
Author(s):  
Martin Čadek ◽  
Marek Krčál ◽  
Lukáš Vokřínek
Keyword(s):  
Extension Problem ◽  
Algorithmic Solvability
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