MIXED FRACTIONAL DIFFERENTIATION OPERATORS IN HÖLDER SPACES DEFINED BY USUAL HÖLDER CONDITION

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class defined by usual Hölder condition

Hardy-Littlewood-Type Theorem for Mixed Fractional Integrals in Hölder Spaces

Indian Journal of Advanced Mathematics - regular ◽

10.54105/ijam.b1105.101221 ◽

2021 ◽

pp. 15-19

Author(s):

TulkinMamatov ◽

◽

Nemat Mustafoev ◽

Dilshod Barakaev ◽

Rano Sabirova ◽

...

Keyword(s):

Fractional Derivative ◽

Fractional Integration ◽

Type Theorem ◽

Fractional Integrals ◽

Power Weight ◽

Hölder Spaces ◽

We study mixed Riemann-Liouville fractional integration operators and mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The obtained are results generalized to the case of Hölder spaces with power weight.

Hardy-Littlewood-Type Theorem for Mixed Fractional Integrals in Hölder Spaces

10.35940/ijam.b1105.101221 ◽

2021 ◽

Vol 1 (2) ◽

pp. 15-19

Author(s):

Tulkin Mamatov ◽

Nemat Mustafoev ◽

Dilshod Barakaev ◽

Rano Sabirova

Keyword(s):

Fractional Derivative ◽

Fractional Integration ◽

Type Theorem ◽

Fractional Integrals ◽

Power Weight ◽

Hölder Spaces ◽

Mapping Properties of Mixed Fractional Differentiation Operators in Hölder Spaces Defined by Usual Hölder Condition

Journal of Computer Science & Computational Mathematics ◽

10.20967/jcscm.2019.02.003 ◽

2019 ◽

Vol 9 (2) ◽

pp. 29-34

Author(s):

T. Mamatov

Keyword(s):

Fractional Differentiation ◽

Hölder Condition ◽

Hölder Spaces ◽

Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels

Journal of Function Spaces ◽

10.1155/2019/8561402 ◽

2019 ◽

Vol 2019 ◽

pp. 1-7

Author(s):

Hussain Al-Qassem ◽

Leslie Cheng ◽

Yibiao Pan

Keyword(s):

Singular Integral ◽

Singular Integrals ◽

Integral Operators ◽

Singular Integral Operators ◽

Hölder Condition ◽

Oscillatory Singular Integral ◽

Hölder Class ◽

Holder Class ◽

Oscillatory Singular Integrals

We prove the uniform L1→L1,∞ and HE1→L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón-Zygmund kernel K(x,y) satisfying a Hölder condition. This Hölder condition appreciably weakens the C1 condition imposed in existing literature.

Approximation of a Function in Hölder Class Using Double Karamata (Kλ,μ) Method

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v13i3.3663 ◽

2020 ◽

Vol 13 (3) ◽

pp. 567-578

Author(s):

H. K. Nigam ◽

Md. Hadish

Keyword(s):

Fourier Series ◽

Best Approximation ◽

Double Fourier Series ◽

Hölder Class ◽

The Best Approximation ◽

Holder Class ◽

Approximation Of A Function

In this paper, we establish a new theorem on the best approximation of a function of two variables belonging to H ̈older class by double Karamata (Kλ,μ) means of its double Fourier series.