Lp-Boundedness of Two Singular Integral Operators of Convolution Type

Musonda, John, 1981- (author): Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM

(creator_code:org_t)

2017-02-11
2016
English.
In: Engineering Mathematics II. - Cham : Springer. - 9783319421049 - 9783319421056

Related links:: http://www.springer....; show more...; https://urn.kb.se/re...; https://doi.org/10.1...; show less...

Abstract Subject headings

We investigate boundedness properties of two singular integral operators defined on Lp-spaces (1 < p < ∞) on the real line, both as convolution operators on Lp(R) and on the spaces Lp(w), where w(x) = 1/2cosh πx/2. It is proved that both operators are bounded on these spaces and estimates of the norms are obtained. This is achieved by first proving boundedness for p = 2 and weak boundedness for p = 1, and then using interpolation to obtain boundedness for 1 < p ≤ 2. To obtain boundedness also for 2 ≤ p < ∞, we use duality in the translation invariant case, while the weighted case is partly based on the expositions on the conjugate function operator in [7].π/2

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

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