2021
DOI: 10.1007/s12220-021-00757-3
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Product Space Singular Integrals with Mild Kernel Regularity

Abstract: We develop product space theory of singular integrals with mild kernel regularity. We study these kernel regularity questions specifically in situations that are very tied to the T1 type arguments and the corresponding structural theory. In addition, our results are multilinear.

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Cited by 5 publications
(9 citation statements)
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“…The modified versions of the standard operators are much more difficult to handle and we are forced to rely on the lemma that these can be written as a sum of the standard ones. However, as it is explained in [3], this will cause a loss in the kernel regularity. Yet another problem appears when dealing with the genuinely multilinear weights.…”
Section: 4mentioning
confidence: 97%
“…The modified versions of the standard operators are much more difficult to handle and we are forced to rely on the lemma that these can be written as a sum of the standard ones. However, as it is explained in [3], this will cause a loss in the kernel regularity. Yet another problem appears when dealing with the genuinely multilinear weights.…”
Section: 4mentioning
confidence: 97%
“…This normalization is an absolute constant away from the correct one since we consider that K 2 × (L 3 ) (1) is the top rectangle in parameters 2 and 3.…”
Section: Now Since We Can Easily Check Thatmentioning
confidence: 99%
“…Let T be a bilinear paraproduct free Calderón-Zygmund operator adapted to Zygmund dilations as in Definition 3.5. Let 1 < p 1 , p 2 < ∞ and 1 2 < p < ∞ with 1 p := 1 p 1 + 1 p 2 . Then we have…”
Section: Introductionmentioning
confidence: 99%
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“…We mention that the required regularity is ω i ∈ Dini 3/2 , i = 1, 2, but the current proofs only give this in the paraproduct free case. To get this low kernel regularity one needs to adapt methods from [3].…”
Section: Remark 45mentioning
confidence: 99%