Trace theorems

1998 ◽  
pp. 197-246
Author(s):  
Victor I. Burenkov
Keyword(s):  
Trace Theorems

Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization

2017 ◽  
Vol 49 (2) ◽  
pp. 1621-1644 ◽  
Author(s):  
Xiaochuan Tian ◽  
Qiang Du
Keyword(s):  
Function Spaces ◽  
Trace Theorems

scholarly journals Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

2017 ◽  
Vol 5 (1) ◽  
pp. 98-115 ◽  
Author(s):  
Eero Saksman ◽  
Tomás Soto
Keyword(s):  
Sobolev Space ◽  
Sobolev Spaces ◽  
Metric Space ◽  
Besov Spaces ◽  
Metric Spaces ◽  
Function Spaces ◽  
First Order ◽  
Trace Theorems ◽  
Euclidean Setting ◽  
Regular Subset

Abstract We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.

scholarly journals A sharp form of the Sobolev trace theorems

1977 ◽  
Vol 25 (1) ◽  
pp. 70-80 ◽  
Author(s):  
Ridgway Scott
Keyword(s):  
Sharp Form ◽  
Trace Theorems

scholarly journals Trace theorems for trees and application to the human lungs

2009 ◽  
Vol 4 (3) ◽  
pp. 469-500 ◽  
Author(s):  
Bertrand Maury ◽  
◽  
Delphine Salort ◽  
Christine Vannier ◽  
◽  
...  
Keyword(s):  
Trace Theorems ◽  
Human Lungs

scholarly journals New tensorial estimates in Besov spaces for time-dependent (2 + 1)-dimensional problems

2014 ◽  
Vol 11 (04) ◽  
pp. 821-908
Author(s):  
Arick Shao
Keyword(s):  
Primary Objective ◽  
Null Cone ◽  
Trace Theorems ◽  
Einstein Vacuum ◽  
Bondi Mass ◽  
Vacuum Spacetime ◽  
Bondi Energy ◽  
Funct Anal ◽  
Invent Math ◽  
Causal Geometry

In this paper, we consider various tensorial estimates in geometric Besov-type norms on a one-parameter foliation of surfaces with evolving geometries. Moreover, we wish to accomplish this with only very weak control on these geometries. Several of these estimates were proved in [S. Klainerman and I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (2005) 437–529; S. Klainerman and I. Rodnianski, Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux, Geom. Funct. Anal. 16(3) (2006) 164–229], but in very specific settings. A primary objective of this paper is to significantly simplify and make more robust the proofs of the estimates. Another goal is to generalize these estimates to more abstract settings. In [S. Alexakis and A. Shao, On the geometry of null cones to infinity under curvature flux bounds, Class. Quantum Grav. 31 (2014) 195012], we will apply these estimates in order to consider a variant of the problem in [S. Klainerman and I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (2005) 437–529], that of a truncated null cone in an Einstein-vacuum spacetime extending to infinity. This analysis will then be used in [S. Alexakis and A. Shao, Bounds on the Bondi energy by a flux of curvature, to appear in J. Eur. Math. Soc.] to study and to control the Bondi mass and the angular momentum under minimal conditions.

QUATERNION TRACE THEOREMS AND FIRST ORDER ELECTRON-MUON SCATTERING

1989 ◽  
Vol 04 (18) ◽  
pp. 1763-1771 ◽  
Author(s):  
P. ROTELLI
Keyword(s):  
Maxwell Equation ◽  
Quantum Electrodynamics ◽  
Muon Scattering ◽  
Standard Result ◽  
First Order ◽  
Trace Theorems

We exhibit the necessary trace theorems for calculations in quaternion quantum electrodynamics. Two independent photon solutions of the Maxwell equation are found, but only one is needed to reproduce the standard result for first order electron-muon scattering.

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