Coincidence of classes of functions defined by the generalized shift operator or by the order of best polynomial approximation

1999 ◽  
Vol 66 (2) ◽  
pp. 190-202
Author(s):  
M. K. Potapov
Keyword(s):  
Polynomial Approximation ◽  
Shift Operator ◽  
Generalized Shift Operator ◽  
Best Polynomial Approximation ◽  
Generalized Shift

On the boundedness of a B-Riesz potential in the generalized weighted B-Morrey spaces

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Rabil Ayazoglu (Mashiyev) ◽  
Javanshir J. Hasanov
Keyword(s):  
Differential Operator ◽  
Shift Operator ◽  
Riesz Potential ◽  
Morrey Spaces ◽  
Generalized Shift Operator ◽  
Bessel Differential Operator ◽  
Generalized Shift

AbstractWe consider the generalized shift operator associated with the Laplace–Bessel differential operator

scholarly journals Some Embeddings into the Morrey and Modified Morrey Spaces Associated with the Dunkl Operator

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Emin V. Guliyev ◽  
Yagub Y. Mammadov
Keyword(s):  
Maximal Operator ◽  
Morrey Space ◽  
Shift Operator ◽  
Morrey Spaces ◽  
Dunkl Operator ◽  
Generalized Shift Operator ◽  
Fractional Maximal Operator ◽  
Generalized Shift

We consider the generalized shift operator, associated with the Dunkl operatorΛα(f)(x)=(d/dx)f(x)+((2α+1)/x)((f(x)-f(-x))/2),α>-1/2. We study some embeddings into the Morrey space (D-Morrey space)Lp,λ,α,0≤λ<2α+2and modified Morrey space (modifiedD-Morrey space)L̃p,λ,αassociated with the Dunkl operator onℝ. As applications we get boundedness of the fractional maximal operatorMβ,0≤β<2α+2, associated with the Dunkl operator (fractionalD-maximal operator) from the spacesLp,λ,αtoL∞(ℝ)forp=(2α+2-λ)/βand from the spacesL̃p,λ,α(ℝ)toL∞(ℝ)for(2α+2-λ)/β≤p≤(2α+2)/β.

On Estimating the Approximation of Locally Summable Functions by Gegenbauer Singular Integrals

2008 ◽  
Vol 15 (2) ◽  
pp. 251-262
Author(s):  
Vagif S. Guliyev ◽  
Elman J. Ibrahimov
Keyword(s):  
Differential Operator ◽  
Singular Integrals ◽  
Shift Operator ◽  
Summable Function ◽  
Generalized Shift Operator ◽  
Order Estimation ◽  
Generalized Shift ◽  
Almost All

Abstract Using the generalized shift operator (GSO) generated by the Gegenbauer differential operator we introduce the notion of a Lebesgue–Gegenbauer (L-G)-point of a summable function 𝑓 on the interval [1,∞) and prove that almost all points of this interval are (L-G)-points of 𝑓. Furthermore, we give an exact (by order) estimation of the approximation of locally summable functions by singular integrals generated by GSO (Gegenbauer singular integrals).

scholarly journals Modulus of smoothness and theorems concerning approximation on compact groups

2003 ◽  
Vol 2003 (20) ◽  
pp. 1251-1260 ◽  
Author(s):  
H. Vaezi ◽  
S. F. Rzaev
Keyword(s):  
Compact Group ◽  
Shift Operator ◽  
Modulus Of Smoothness ◽  
Compact Groups ◽  
Jackson Type ◽  
Generalized Shift Operator ◽  
Generalized Shift

We consider the generalized shift operator defined by(Shuf)(g)=∫Gf(tut−1g)dton a compact groupG, and by using this operator, we define “spherical” modulus of smoothness. So, we prove Stechkin and Jackson-type theorems.

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