Plancherel Type Estimates and Sharp Spectral Multipliers

By Xuan Thinh Duong, El-Maati Ouhabaz, Adam S. Sikora. 2002

293 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/abffbbc271db21600c165b7d92c0715e75f42fb9

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In Applied Mathematics

1. Dachun Yang
2. Xuan Thinh Duong
3. Sibei Yang
4. Lixin Yan
5. T. Coulhon
6. Adam S. Sikora
7. Robert S. Strichartz
8. Gerard Kerkyacharian

In Mathematical Physics

1. Dachun Yang
2. Xuan Thinh Duong
3. Lixin Yan
4. Sibei Yang
5. T. Coulhon
6. Adam S. Sikora
7. Robert S. Strichartz
8. El-Maati Ouhabaz

Citations in the corpus

• Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means (2012, background): “We refer the reade r to [2, 12, 14, 15, 16, 17, 21, 23, 24, 25, 26, 27, 28, 30, 32, 34, 44, 47, 48, 50, 53, 54, 56, 58, 59, 61, 63, 64] and the references therein.”
• Gaussian heat kernel upper bounds via the Phragmén–Lindelöf theorem (2006, unknown): “…of Bochner– Riesz means or boundedness of spectral multipliers, as well as problems related to maximal regularity properties (see, for example, the articles [ 1 , 2 , 4 , 15 , 16 , 20 – 23 , 31 , for all t > 0, x, y ranging in the space where the operator acts, for an appropriate function V .”
• Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, background): “The calculus of smooth operators is in the spirit of [17, 45] and will be needed in most part of this article, including the construction of frames and the Littlewood-Paley theory, while the nonsmooth calculus will be needed for estimation of the kernels of the spectral projectors and lower bound es”
• Analysis of degenerate elliptic operators of Grušin type (2006, unknown): “1 of [14].”
• Restriction and spectral multiplier theorems on asymptotically conic manifolds (2010, unknown): “In region A this was previously known ([Duong et al. 2002]; see also Proposition 2.”
• Gaussian estimates and Lp-boundedness of Riesz means (2002, methodology): “In the rest of the proof we will follow an idea which was used in [22] and [ 20 ].”
• Laplacians on fractals with spectral gaps have nicer Fourier series (2005, methodology): “The next ingredient in the argument is a “generic” spectral multiplier theorem of Duong, Ouhabaz and Sikora ([ DOS ], Theorem 6.2), which yields σNf → f in Lq if f ∈ Lq ,1 ≤ q DOS ] gives the desired bounds on the spectral multiplier operator.”
• Musielak–Orlicz–Hardy Spaces Associated with Operators and Their Applications (2012, background): “1) is bounded on various function spaces on X , which was extensively studied (see, for example, [2, 3, 10, 21, 33, 38, 78, 30] and their references).”
• COMPARISON OF THE CLASSICAL BMO WITH THE BMO SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS (2006, background): “For example such multipliers were studied in [1, 6, 14, 21, 24, 26].”
• Weighted norm inequalities, Gaussian bounds and sharp spectral multipliers (2010, methodology): “The aim of this paper is to extend the study of sharp spectral multipliers in [18] to the setting of weighted L spaces.”