Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization

2017 ◽  
Vol 49 (2) ◽  
pp. 1621-1644 ◽  
Author(s):  
Xiaochuan Tian ◽  
Qiang Du
2017 ◽  
Vol 5 (1) ◽  
pp. 98-115 ◽  
Author(s):  
Eero Saksman ◽  
Tomás Soto

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.


2018 ◽  
Vol 25 (5) ◽  
pp. 729-740
Author(s):  
Hadis Pazandeh ◽  
Fereshteh Sady
Keyword(s):  

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.


1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha

1998 ◽  
Vol 24 (1) ◽  
pp. 113
Author(s):  
Shi ◽  
Thomson
Keyword(s):  

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