The boundedness and the fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients

Deundyak, V. M.; Miroshnikova, Elena

doi:10.3103/s1066369x12070018

Cited by 3 publications

(1 citation statement)

References 9 publications

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“…New broad class of operators with kernels of compact type including the set of SO(n)-invariant kernels was introduced and investigated in [3]. In [4] the results of [3] on boundedness and Fredholm property are expanded to the case of operators with anisotropically homogeneous kernels. The purpose of the present paper is to extend results related to boundedness and invertibility to the case of weighted L p -spaces.…”

Section: Introductionmentioning

confidence: 99%

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

Miroshnikova¹

2014

AIP Conference Proceedings

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In weighted space L p (R n , ρ), 1 < p < ∞, a new broad class of integral operators with anisotropically homogeneous kernels is investigated. For such operators boundedness theorem is proved. Also the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type is considered. For elements of the algebra symbolic calculation is constructed, the invertibility criterion is obtained in terms of operator symbol.

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Section: Introductionmentioning

confidence: 99%

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

Miroshnikova¹

2014

AIP Conference Proceedings

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Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the L2 Space on the Heisenberg Group

Denisenko

Deundyak

2020

Proc. Steklov Inst. Math.

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Фредгольмовость Интегральных Операторов С Однородными Ядрами Компактного Типа В $L_2$-Пространстве На Группе Гейзенберга

Денисенко¹,

Denisenko

Деундяк³

et al. 2020

Trudy Mat. Inst. Steklova

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Рассматривается группа Гейзенберга $\mathbb H_n$ с нормой Кораньи. В пространстве $L_2(\mathbb H_n)$ вводятся интегральные операторы с однородными ядрами компактного типа и мультипликативно слабо осциллирующими коэффициентами. Для $C^*$-алгебры с единицей $\mathfrak W(\mathbb H_n)$, порожденной такими операторами, строится символическое исчисление, и в его терминах формулируются необходимые и достаточные условия фредгольмовости операторов из $\mathfrak W(\mathbb H_n)$.

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The boundedness and the fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients

Cited by 3 publications

References 9 publications

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

Boundedness and invertibility of multidimensional integral operators with anisotropically homogeneous kernels in weighted Lp-spaces

Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the L2 Space on the Heisenberg Group

Фредгольмовость Интегральных Операторов С Однородными Ядрами Компактного Типа В $L_2$-Пространстве На Группе Гейзенберга

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