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

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 ◽  
Function Of Two Variables ◽  
Holder 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.

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

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 ◽  
Function Of Two Variables ◽  
Holder 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.

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

2019 ◽  
Author(s):  
T. Mamatov ◽  
R. Sabirova ◽  
D. Barakaev
Keyword(s):  
Fractional Derivative ◽  
Fractional Differentiation ◽  
Hölder Condition ◽  
Hölder Spaces ◽  
Main Interest ◽  
Hölder Class ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Holder Spaces

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

scholarly journals Fractional Type Operators in Weighted Generalized Hölder Spaces

1994 ◽  
Vol 1 (5) ◽  
pp. 537-559
Author(s):  
S. G. Samko ◽  
Z. U. Mussalaeva
Keyword(s):  
Convolution Type ◽  
Fractional Integrals ◽  
Hölder Spaces ◽  
Continuity Modulus ◽  
Type Spaces ◽  
Holder Spaces ◽  
Fractional Type

Abstract Weighted Zygmund type estimates are obtained for the continuity modulus of some convolution type integrals. In the case of fractional integrals this is strengthened to a result on isomorphism between certain weighted generalized Hölder type spaces.

scholarly journals Fractional integrals and hypersingular integrals in variable order Hölder spaces on homogeneous spaces

2010 ◽  
Vol 8 (3) ◽  
pp. 215-244 ◽  
Author(s):  
Natasha Samko ◽  
Stefan Samko ◽  
Boris Vakulov
Keyword(s):  
Homogeneous Spaces ◽  
Measure Zero ◽  
Fractional Integrals ◽  
Variable Order ◽  
Hölder Spaces ◽  
Continuity Modulus ◽  
Hypersingular Integrals ◽  
Potential Operators ◽  
Complex Valued ◽  
Holder Spaces

We consider non-standard Hölder spacesHλ(⋅)(X)of functionsfon a metric measure space (X, d, μ), whose Hölder exponentλ(x) is variable, depending onx∈X. We establish theorems on mapping properties of potential operators of variable orderα(x), from such a variable exponent Hölder space with the exponentλ(x) to another one with a “better” exponentλ(x) +α(x), and similar mapping properties of hypersingular integrals of variable orderα(x) from such a space into the space with the “worse” exponentλ(x) −α(x) in the caseα(x) <λ(x). These theorems are derived from the Zygmund type estimates of the local continuity modulus of potential and hypersingular operators via such modulus of their densities. These estimates allow us to treat not only the case of the spacesHλ(⋅)(X), but also the generalized Hölder spacesHw(⋅,⋅)(X)of functions whose continuity modulus is dominated by a given functionw(x, h),x∈X, h> 0. We admit variable complex valued ordersα(x), whereℜα(x)may vanish at a set of measure zero. To cover this case, we consider the action of potential operators to weighted generalized Hölder spaces with the weightα(x).

Solvability in Hölder spaces of an integral equation which models dynamics of the capillary rise

2020 ◽  
Vol 490 (1) ◽  
pp. 124237
Author(s):  
Hanna Okrasińska-Płociniczak ◽  
Łukasz Płociniczak ◽  
Juan Rocha ◽  
Kishin Sadarangani
Keyword(s):  
Integral Equation ◽  
Capillary Rise ◽  
Hölder Spaces ◽  
Holder Spaces
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