scholarly journals Kolmogorov type inequalities for hypersingular integrals with sign-alternating characteristic

2021 ◽  
Vol 18 ◽  
pp. 18
Author(s):  
V.F. Babenko ◽  
D.A. Levchenko
Keyword(s):  
Multivariate Functions ◽  
Hölder Spaces ◽  
Kolmogorov Type ◽  
Hypersingular Integrals ◽  
Holder Spaces

New sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of the form $\Omega(t) = \mathrm{sgn} \prod\limits_{k=1}^m t_k$ for multivariate functions from Hölder spaces are obtained.

More on Hypersingular Integrals and Embeddings into Hölder Spaces

2016 ◽  
pp. 439-454
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi ◽  
Humberto Rafeiro ◽  
Stefan Samko
Keyword(s):  
Hölder Spaces ◽  
Hypersingular Integrals ◽  
Holder Spaces

scholarly journals PROPERTIES OF INTEGRALS WHICH HAVE THE TYPE OF DERIVATIVES OF VOLUME POTENTIALS FOR DEGENERATED $\overrightarrow{2\lowercase{b}}$ - PARABOLIC EQUATION OF KOLMOGOROV TYPE

2021 ◽  
Vol 9 (2) ◽  
pp. 7-21
Author(s):  
V. Dron' ◽  
I. Medyns'kyi
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Homogeneous Equation ◽  
Hölder Spaces ◽  
Kolmogorov Type ◽  
Estimates Of Solutions ◽  
The Cauchy Problem ◽  
The Given ◽  
Holder Spaces ◽  
Derivatives Of

In weight Holder spaces it is studied the smoothness of integrals, which have the structure and properties of derivatives of volume potentials which generated by fundamental solution of the Cauchy problem for degenerated $\overrightarrow{2b}$-parabolic equation of Kolmogorov type. The coefficients in this equation depend only on the time variable. Special distances and norms are used for constructing of the weight Holder spaces. The results of the paper can be used for establishing of the correct solvability of the Cauchy problem and estimates of solutions of the given non-homogeneous equation in corresponding weight Holder 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).

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

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

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by L-modulus of smoothness

2019 ◽  
Vol 276 (2) ◽  
pp. 636-657 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Júlio S. Neves ◽  
Bohumír Opic
Keyword(s):  
Modulus Of Smoothness ◽  
Sobolev Type ◽  
Hölder Spaces ◽  
Sobolev Type Spaces ◽  
Type Spaces ◽  
Holder Spaces

scholarly journals Holder spaces of quasiconformal mappings

2004 ◽  
Vol 75 (89) ◽  
pp. 87-94
Author(s):  
Leonid Kovalev
Keyword(s):  
Quasiconformal Mappings ◽  
Hölder Spaces ◽  
Holder Spaces
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