Electronic ISBN:  9781470401092 
Product Code:  MEMO/110/530.E 
List Price:  $42.00 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 110; 1994; 126 ppMSC: Primary 42;
In this work, Han and Sawyer extend LittlewoodPaley theory, Besov spaces, and TriebelLizorkin 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 bmoment, and LittlewoodPaley characterizations of Besov and TriebelLizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.
ReadershipResearch mathematicians.

Table of Contents

Chapters

1. Introduction

2. $T^{1}_N$ is a CalderónZygmund operator

3. The Calderóntype reproducing formula on spaces of homogeneous type

4. The Besov and TriebelLizorkin 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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In this work, Han and Sawyer extend LittlewoodPaley theory, Besov spaces, and TriebelLizorkin 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 bmoment, and LittlewoodPaley characterizations of Besov and TriebelLizorkin 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 CalderónZygmund operator

3. The Calderóntype reproducing formula on spaces of homogeneous type

4. The Besov and TriebelLizorkin 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 $\dot {F}^{\alpha , q}_p$