1988
DOI: 10.1017/s0308210500024860
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A note on the Stieltjes transformation

Abstract: SynopsisA necessary and sufficient condition for the boundedness of the generalised Stieltjes transformation on weighted Lebesgue spaces is obtained and applied to extend the Hilbert double series theorem.

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Cited by 19 publications
(10 citation statements)
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“…For the case q ≥ 1 this result is due to G. Sinnamon [10], who complemented a previous result of K. F. Andersson [1] concerning e.g. the case 1 ≤ p ≤ q ≤ ∞, λ > 0.…”
Section: Remark 42supporting
confidence: 65%
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“…For the case q ≥ 1 this result is due to G. Sinnamon [10], who complemented a previous result of K. F. Andersson [1] concerning e.g. the case 1 ≤ p ≤ q ≤ ∞, λ > 0.…”
Section: Remark 42supporting
confidence: 65%
“…In this section we give a new proof of an extended form of a result of G. Sinnamon . Proposition Let λ>0, 1p<, 0<q<p, 1r=1q1p and suppose that u(x) and v(x) are non‐negative extended real valued functions defined on (0, ∞).…”
Section: On a Results Of Sinnamon Concerning The Stieltjes Transformmentioning
confidence: 99%
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