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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

Kernel operators and their boundedness from weighted Sobolev space to weighted Lebesgue space

Aigerim KALYBAY
Ryskul OINAROV
Sayfa
301–315
Yayın Tarihi
2022-11-04
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The crucial step in the proof of the main result is to use theequivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, for a wide class of integral operators, we consider the problem of their boundedness from aweighted Sobolev space to a weighted Lebesgue space.
📊
Temel Bulgular & Veri:In this paper, for a wide class of integral operators, we consider the problem of their boundedness from aweighted Sobolev space to a weighted Lebesgue space.
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Sonuç & Katkı:The crucial step in the proof of the main result is to use theequivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, for a wide class of integral operators, we consider the problem of their boundedness from aweighted Sobolev space to a weighted Lebesgue space. The crucial step in the proof of the main result is to use theequivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.

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Bu Makaleye Atıf Yap

KALYBAY, A., OINAROV, R. (2022). Kernel operators and their boundedness from weighted Sobolev space to weighted Lebesgue space. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 301–315. https://ajindex.com/articles/607659

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Kaynakça (10)

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  3. Kufner A, Persson LE. Weighted Inequalities of Hardy type. London, UK: World Scientific, 2003
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  8. Oinarov R. Boundedness and compactness in weighted Lebesgue spaces of integral operators with variable integration limits. Siberian Math J 2011; 52: 1042-1055
  9. Prokhorov DV, Stepanov VD, Ushakova EP. Hardy-Steklov integral operators. Part I. Proc Steklov Inst Math 2018; 300: 1-111
  10. Stepanov VD, Ushakova EP. Kernel operators with variable intervals of integration in Lebesgue spaces and applications. Math Inequal Appl 2010; 13: 449-510.