Asymmetry of Convolution Norms on Lie Groups

A. H. Dooley; Sanjiv Kumar Gupta; Fulvio Ricci

doi:10.1006/jfan.2000.3573

Asymmetry of Convolution Norms on Lie Groups

A. H. Dooley^*, Sanjiv Kumar Gupta, Fulvio Ricci

^*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلة › Article › مراجعة النظراء

7 اقتباسات (Scopus)

ملخص

We prove that on most connected non-commutative Lie groups there exists a convolution operator which is bounded on L^p but unbounded on L^q for every q not belonging to the interval with endpoints 2 and p. Furthermore, the kernel of such an operator can be supported on an arbitrary neighbourhood of the identity.

اللغة الأصلية	English
الصفحات (من إلى)	399-416
عدد الصفحات	18
دورية	Journal of Functional Analysis
مستوى الصوت	174
رقم الإصدار	2
المعرِّفات الرقمية للأشياء	https://doi.org/10.1006/jfan.2000.3573
حالة النشر	Published - يوليو 10 2000
منشور خارجيًا	نعم

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10.1006/jfan.2000.3573

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abstract = "We prove that on most connected non-commutative Lie groups there exists a convolution operator which is bounded on Lp but unbounded on Lq for every q not belonging to the interval with endpoints 2 and p. Furthermore, the kernel of such an operator can be supported on an arbitrary neighbourhood of the identity.",

author = "Dooley, {A. H.} and Gupta, {Sanjiv Kumar} and Fulvio Ricci",

note = "Funding Information: 1We thank Michael Cowling and Garth Gaudry for useful discussion in the development of this work. We acknowledge the support of the Australian Research Council and of the Italian MURST. The last-named author thanks the School of Mathematics UNSW for its hospitality while this work was being done.",

year = "2000",

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doi = "10.1006/jfan.2000.3573",

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T1 - Asymmetry of Convolution Norms on Lie Groups

AU - Dooley, A. H.

AU - Gupta, Sanjiv Kumar

AU - Ricci, Fulvio

N1 - Funding Information: 1We thank Michael Cowling and Garth Gaudry for useful discussion in the development of this work. We acknowledge the support of the Australian Research Council and of the Italian MURST. The last-named author thanks the School of Mathematics UNSW for its hospitality while this work was being done.

PY - 2000/7/10

Y1 - 2000/7/10

N2 - We prove that on most connected non-commutative Lie groups there exists a convolution operator which is bounded on Lp but unbounded on Lq for every q not belonging to the interval with endpoints 2 and p. Furthermore, the kernel of such an operator can be supported on an arbitrary neighbourhood of the identity.

AB - We prove that on most connected non-commutative Lie groups there exists a convolution operator which is bounded on Lp but unbounded on Lq for every q not belonging to the interval with endpoints 2 and p. Furthermore, the kernel of such an operator can be supported on an arbitrary neighbourhood of the identity.

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U2 - 10.1006/jfan.2000.3573

DO - 10.1006/jfan.2000.3573

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Asymmetry of Convolution Norms on Lie Groups

ملخص

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