The convergence rate of truncated hypersingular integrals generated by the modified Poisson semigroup
| Autor: | Sinem Sezer Evcan, Selim Çobanoğlu, Melih Eryigit |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Semigroup
Applied Mathematics lcsh:Mathematics 010102 general mathematics Order (ring theory) Function (mathematics) Rate of convergence Poisson distribution Differential operator lcsh:QA1-939 01 natural sciences Inversion (discrete mathematics) Flett potentials 010101 applied mathematics Combinatorics symbols.namesake Poisson semigroup Truncated hypersingular integrals symbols Discrete Mathematics and Combinatorics 0101 mathematics Analysis Bessel function Mathematics |
| Zdroj: | Journal of Inequalities and Applications, Vol 2020, Iss 1, Pp 1-12 (2020) |
| DOI: | 10.1186/s13660-020-02468-9 |
| Popis: | Hypersingular integrals have appeared as effective tools for inversion of multidimensional potential-type operators such as Riesz, Bessel, Flett, parabolic potentials, etc. They represent (at least formally) fractional powers of suitable differential operators. In this paper the family of the so-called “truncated hypersingular integral operators” $\mathbf{D}_{\varepsilon }^{\alpha }f$ D ε α f is introduced, that is generated by the modified Poisson semigroup and associated with the Flett potentials F α φ = ( E + − Δ ) − α φ ($0 0 < α < ∞ , $\varphi \in L_{p}(\mathbb{R}^{n})$ φ ∈ L p ( R n ) ). Then the relationship between the order of “$L_{p}$ L p -smoothness” of a function f and the “rate of $L_{p}$ L p -convergence” of the families $\mathbf{D}_{\varepsilon }^{\alpha } \mathcal{F}^{\alpha }f$ D ε α F α f to the function f as $\varepsilon \rightarrow 0^{+}$ ε → 0 + is also obtained. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
| Nepřihlášeným uživatelům se plný text nezobrazuje | K zobrazení výsledku je třeba se přihlásit. |