scholarly journals An embedding theorem for function spaces

1966 ◽  
Vol 19 (2) ◽  
pp. 243-251 ◽  
Author(s):  
Colin Clark
Keyword(s):  
Function Spaces ◽  
Embedding Theorem

scholarly journals Infinite combinatorics in function spaces: Category methods

2009 ◽  
Vol 86 (100) ◽  
pp. 55-73 ◽  
Author(s):  
N.H. Bingham ◽  
A.J. Ostaszewski
Keyword(s):  
Function Spaces ◽  
Embedding Theorem ◽  
Regularly Varying Functions ◽  
Infinite Combinatorics ◽  
Regularly Varying ◽  
Special Case ◽  
Null Set

The infinite combinatorics here give statements in which, from some sequence, an infinite subsequence will satisfy some condition - for example, belong to some specified set. Our results give such statements generically - that is, for 'nearly all' points, or as we shall say, for quasi all points - all off a null set in the measure case, or all off a meagre set in the category case. The prototypical result here goes back to Kestelman in 1947 and to Borwein and Ditor in the measure case, and can be extended to the category case also. Our main result is what we call the Category Embedding Theorem, which contains the Kestelman-Borwein-Ditor Theorem as a special case. Our main contribution is to obtain function wise rather than point wise versions of such results. We thus subsume results in a number of recent and related areas, concerning e.g., additive, subadditive, convex and regularly varying functions.

Function Spaces and Nonsymmetric Norm Preserving Maps

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

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

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?.

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces

PREVALENT PROPERTIES IN FUNCTION SPACES

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