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Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces

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Electronic ISBN: 978-1-4704-0109-2
Product Code: MEMO/110/530.E
List Price: $42.00 MAA Member Price:$37.80
AMS Member Price: $25.20 Click above image for expanded view Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces Available Formats:  Electronic ISBN: 978-1-4704-0109-2 Product Code: MEMO/110/530.E  List Price:$42.00 MAA Member Price: $37.80 AMS Member Price:$25.20
• Book Details

Memoirs of the American Mathematical Society
Volume: 1101994; 126 pp
MSC: Primary 42;

In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calderón reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

Research mathematicians.

• Chapters
• 1. Introduction
• 2. $T^{-1}_N$ is a Calderón-Zygmund operator
• 3. The Calderón-type reproducing formula on spaces of homogeneous type
• 4. The Besov and Triebel-Lizorkin spaces on spaces of homogeneous type
• 5. The T1 theorems for $\dot {B}^{\alpha , q}_p$ and $\dot {F}^{\alpha , q}_p$
• 6. Atomic decomposition of $\dot {B}^{\alpha , q}_p$ and $\dot {F}^{\alpha , q}_p$
• 7. Duality and interpolation of $\dot {B}^{\alpha , q}_p$ and $\dot {F}^{\alpha , q}_p$
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Volume: 1101994; 126 pp
MSC: Primary 42;

In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calderón reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

• 2. $T^{-1}_N$ is a Calderón-Zygmund operator
• 5. The T1 theorems for $\dot {B}^{\alpha , q}_p$ and $\dot {F}^{\alpha , q}_p$
• 6. Atomic decomposition of $\dot {B}^{\alpha , q}_p$ and $\dot {F}^{\alpha , q}_p$
• 7. Duality and interpolation of $\dot {B}^{\alpha , q}_p$ and $\dot {F}^{\alpha , q}_p$