Some inequalities in function spaces and their application to the study of the convergence of variational processes

Four Papers on Functions of Real Variables - American Mathematical Society Translations: Series 2 ◽

10.1090/trans2/081/01 ◽

1969 ◽

pp. 1-66 ◽

Cited By ~ 3

Author(s):

V. P. Il′in

Keyword(s):

Function Spaces

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Function spaces between crystal space and Fourier-transform space

Zeitschrift für Kristallographie ◽

10.1524/zkri.1959.112.1-6.22 ◽

1959 ◽

Vol 112 (1-6) ◽

pp. 22-32 ◽

Cited By ~ 3

Author(s):

A. L. Patterson

Keyword(s):

Fourier Transform ◽

Function Spaces ◽

Crystal Space

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Function Spaces and Nonsymmetric Norm Preserving Maps

Bulletin of the Belgian Mathematical Society - Simon Stevin ◽

10.36045/bbms/1547780432 ◽

2018 ◽

Vol 25 (5) ◽

pp. 729-740

Author(s):

Hadis Pazandeh ◽

Fereshteh Sady

Keyword(s):

Function Spaces

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

Filomat ◽

10.2298/fil1908457p ◽

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?.

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