Norm inequalities involving upper bounds for certain matrix operators in Orlicz-type sequence spaces

2018 ◽  
Vol 27 (3) ◽  
pp. 761-779
Author(s):  
Atanu Manna
Keyword(s):  
Upper Bounds ◽  
Sequence Spaces ◽  
Norm Inequalities ◽  
Matrix Operators ◽  
Type Sequence

Estimation of upper bounds of certain matrix operators on Binomial weighted sequence spaces

2020 ◽  
Vol 5 (4) ◽  
pp. 1376-1389
Author(s):  
Taja Yaying ◽  
Bipan Hazarika ◽  
S. A. Mohiuddine ◽  
M. Mursaleen
Keyword(s):  
Upper Bounds ◽  
Sequence Spaces ◽  
Weighted Sequence ◽  
Matrix Operators

scholarly journals Optimality of the rearrangement inequality with applications to Lorentz-type sequence spaces

2018 ◽  
pp. 127-132
Author(s):  
Fernando Albiac ◽  
José L. Ansorena ◽  
Denny Leung ◽  
Ben Wallis
Keyword(s):  
Sequence Spaces ◽  
Rearrangement Inequality ◽  
Type Sequence

scholarly journals Basis and regularity properties of ( p , q )-trigonometric functions and the decay of ( p , q )-Fourier coefficients

2018 ◽  
Vol 474 (2210) ◽  
pp. 20170548
Author(s):  
David E. Edmunds ◽  
Houry Melkonian
Keyword(s):  
Lebesgue Space ◽  
Fourier Coefficients ◽  
Upper Bounds ◽  
Sequence Spaces ◽  
Trigonometric Functions ◽  
Fourier Sine ◽  
Regularity Properties

The basis and regularity properties of the generalized trigonometric functions sin p , q and cos p , q are investigated. Upper bounds for the Fourier coefficients of these functions are given. Conditions are obtained under which the functions cos p , q generate a basis of every Lebesgue space L r (0,1) with 1 < r < ∞ ; when q is the conjugate of p , it is sufficient to require that p ∈[ p 1 , p 2 ], where p 1 <2 and p 2 >2 are calculable numbers. A comparison is made of the speed of decay of the Fourier sine coefficients of a function in Lebesgue and Lorentz sequence spaces with that of the corresponding coefficients with respect to the functions sin p , q . These results sharpen previously known ones.

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