Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent
2003 ◽
Vol 10
(1)
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pp. 145-156
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Keyword(s):
Abstract In the weighted Lebesgue space with variable exponent the boundedness of the Calderón–Zygmund operator is established. The variable exponent 𝑝(𝑥) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ρ(𝑥) = |𝑥 – 𝑥0| β is related only to the value 𝑝(𝑥0). The mapping properties of Cauchy singular integrals defined on the Lyapunov curve and on curves of bounded rotation are also investigated within the framework of the above-mentioned weighted space.
2012 ◽
Vol 20
(3)
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pp. 5-20
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2003 ◽
Vol 1
(1)
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pp. 45-59
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2010 ◽
Vol 25
(1)
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pp. 69-77
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2011 ◽
Vol 14
(3)
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