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Calderon-Zygmund Operators and Singular Integrals |
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PP: 97-107 |
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doi:10.18576/amis/150112
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Author(s) |
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Mykola Yaremenko,
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Abstract |
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| In this article, we establish conditions on continuous restrictively bounded linear mapping T from S to S′ associated with the kernel K under which the operator T extends to a bounded operator T : Lp Rl → Lp Rl. Next, we generalize the interpolation theorem for new functional classes, we show that bounded operator T defined, whose kernel satisfies the standard conditions, is bounded
with respect to convex seminorm, so, an inequality M ̃ 1 −1 M ̃ 1 (|T ( f )|)μ ≤ A1 M ̃ 1 −1 M ̃ 1 (| f |)μ holds for the constant A1 that depends only on A, M1, M2.
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