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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
The crucial step in the proof of the main result is to use the equivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, for a wide class of integral operators, we consider the problem of their boundedness from a weighted Sobolev space to a weighted Lebesgue space.
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Key Findings & Data:In this paper, for a wide class of integral operators, we consider the problem of their boundedness from a weighted Sobolev space to a weighted Lebesgue space.
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Conclusion & Impact:The crucial step in the proof of the main result is to use the equivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Integral operator · kernel · weighted Lebesgue space
Abstract
In this paper, for a wide class of integral operators, we consider the problem of their boundedness from a weighted Sobolev space to a weighted Lebesgue space. The crucial step in the proof of the main result is to use the equivalence of the basic inequality and certain Hardy-type inequality, so we first state and prove this equivalence.
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Cite This Article
KALYBAY, A., OINAROV, R. (2019). 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/215005