L2 multipliers with power weights

Muckenhoupt, Benjamin; Wheeden, Richard L.; Young, Wo-Sang

doi:10.1016/0001-8708(83)90072-5

Cited by 22 publications

(20 citation statements)

References 18 publications

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“…To finish the proof of the lemma, all we have to do is approximate each gnk by a function /" G §oo in both the L2 norm and L^p_x norm. This is possible because of Theorem (6.1) of [2]. This completes the proof of Lemma (2.5) and hence the proof of Theorem (1.2).…”

supporting

confidence: 67%

“…To prove Theorem (1.2) we first observe that (1.3) implies that m G U°. This can be shown in exactly the same way as in the proof of Theorem (2.2) in [2]. The rest of the proof is contained in the following lemmas.…”

mentioning

confidence: 59%

“…This is a continuation of our previous work with R. L. Wheeden on multipliers for weighted Lp spaces [2,3]. The underlying space we consider here will either be the line R or the circle [-77,w]; / and / will denote the Fourier transform and inverse Fourier transform of/.…”

mentioning

confidence: 82%

“…In [2] we characterized multipliers for L2., y ^ 2k -1, k a positive integer. Results for the line and the circle are analogues of each other.…”

mentioning

confidence: 99%

“…The first term on the right is equal to log n. The second is majorized by \\/nxt/t dt, which is less than 2 for x G [1,2]. By integration by parts, the third term is equal to…”

mentioning

confidence: 99%

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𝐿^{𝑝} multipliers with weight 𝑥^{𝑘𝑝-1}

Muckenhoupt¹,

Young²

1983

Trans. Amer. Math. Soc.

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Abstract. Let k be a positive integer and 1 < p < oo. It is shown that if T is a multiplier operator on Lp of the line with weight | x \kp~\ then Tf equals a constant times/almost everywhere. This does not extend to the periodic case since m(j) = l/j,j ¥* 0, is a multiplier sequence for Lp of the circle with weight |x|*''_l. A necessary and sufficient condition is derived for a sequence m(j) to be a multiplier on L2 of the circle with weight | x |2/t~'.

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supporting

confidence: 67%

mentioning

confidence: 59%

mentioning

confidence: 82%

“…In [2] we characterized multipliers for L2., y ^ 2k -1, k a positive integer. Results for the line and the circle are analogues of each other.…”

mentioning

confidence: 99%

“…The first term on the right is equal to log n. The second is majorized by \\/nxt/t dt, which is less than 2 for x G [1,2]. By integration by parts, the third term is equal to…”

mentioning

confidence: 99%

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