Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds

Ricci, Fulvio; Stein, Elias M.

doi:10.1016/0022-1236(89)90057-8

Cited by 58 publications

(40 citation statements)

References 7 publications

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“…We prove a similar result as in [C2,RS], for an analytic family of fractional integrals along the parabola S|, in which the operators Sy can be embedded. The convolution kernel of Syz is obtained by taking -z -1 transverse derivatives of arclength measure on the parabola, multiplied by \t\y, and doing so in a homogeneous way.…”

Section: Introductionsupporting

confidence: 73%

Strong Type Endpoint Bounds for Analytic Families of Fractional Integrals

Grafakos¹

1993

Proceedings of the American Mathematical Society

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Section: Introductionsupporting

confidence: 73%

Strong Type Endpoint Bounds for Analytic Families of Fractional Integrals

Grafakos¹

1993

Proceedings of the American Mathematical Society

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“…For example, surface measures on analytic manifolds which generate G were shown to be U -improving in [9]. In [10] it was shown that if g was a regular element, then fj, g * U C L terms of use, available at https://www.cambridge.org/core/terms.…”

Section: Jg Jgmentioning

confidence: 99%

Pointwise estimates of the size of characters of compact Lie groups

Hare¹,

Wilson²,

Yee³

2000

J Aust Math Soc A

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Pointwise bounds for characters of representations of the classical, compact, connected, simple Lie groups are obtained which allow us to study the singularity of central measures. For example, we find the minimal integer k such that any continuous orbital measure convolved with itself k times belongs to L 2 . We also prove that if k = rank G then /i 2 * e L x for all central, continuous measures \i. This improves upon the known classical result which required the exponent to be the dimension of the group G.2000 Mathematics subject classification: primary 43A80; secondary 22E46,43A65.

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“…Taking account of Proposition 2 (p.332 in [9]), we note that R λ (ξ) = Finally, by (6) it follows that, for Re(z) = − n +…”

Section: The Main Resultsmentioning

confidence: 99%

L^p-L^qestimates for some convolution operators with singular measures on the Heisenberg group

Godoy

Rocha

2013

Colloq. Math.

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Abstract. We consider the Heisenberg group H n = C n ×R. Let ν be the Borel measure on H n defined by ν(E) = C n χ E (w, ϕ(w)) η(w)dw, where ϕ(w) = n j=1 a j |w j | 2 , w = (w 1 , ..., wn) ∈ C n , a j ∈ R, and η(w) = η 0 |w| 2 with η 0 ∈ C ∞ c (R). In this paper we characterize the set of pairs (p, q) such that the convolution operator with ν isWe also obtain L p -improving properties of measures supported on the graph of the function ϕ(w) = |w| 2m .

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Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds

Cited by 58 publications

References 7 publications

Strong Type Endpoint Bounds for Analytic Families of Fractional Integrals

Strong Type Endpoint Bounds for Analytic Families of Fractional Integrals

Pointwise estimates of the size of characters of compact Lie groups

L^p-L^qestimates for some convolution operators with singular measures on the Heisenberg group

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Harmonic analysis on nilpotent groups and singular integrals. III. Fractional integration along manifolds

Cited by 58 publications

References 7 publications

Strong Type Endpoint Bounds for Analytic Families of Fractional Integrals

Strong Type Endpoint Bounds for Analytic Families of Fractional Integrals

Pointwise estimates of the size of characters of compact Lie groups

Lp-Lqestimates for some convolution operators with singular measures on the Heisenberg group

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Product

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L^p-L^qestimates for some convolution operators with singular measures on the Heisenberg group