Calderon-Zygmund capacities and operators on nonhomogeneous spaces / Alexander Volberg.

Format:

• Book

Author/Creator:

• Volberg, Alexander, 1956-

Series:

• Regional conference series in mathematics ; no. 100.
• Regional conference series in mathematics

Language:

English

Subjects (All):

• Calderón-Zygmund operator.

Genre:

• Conference papers and proceedings.

Physical Description:

iv, 167 pages ; 25 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2003.

Contents:

• Chapter 2. Preliminaries on Capacities 7
• Chapter 3. Localization of Newton and Riesz Potentials 11
• 3.1. Localization lemmas 11
• 3.2. A building block for the construction of special measures 13
• 3.3. Localization on special cubes 13
• 3.4. Modification of distribution S. Construction of auxiliary measures 14
• 3.5. Ahlfors balls 15
• 3.6. The principal estimate for auxiliary measures 16
• Chapter 4. From Distribution to Measure. Carleson Property 21
• Chapter 5. Potential Neighborhood that has Properties (3.13)-(3.14) 25
• 5.1. Capacities with Calderon-Zygmund (CZ) kernels 26
• 5.2. Variational capacity and extremal measures 33
• 5.3. L[superscript p] theory of nonhomogeneous CZ operators. Measure of order m 42
• 5.4. Riesz and Cauchy kernels: [gamma]+ [characters not reproducible] [gamma subscript op] 45
• 5.5. Cauchy kernel and analytic capacity 47
• Chapter 6. The Tree of the Proof 51
• Chapter 7. The First Reduction to Nonhomogeneous Tb Theorem 55
• Chapter 8. The Second Reduction 61
• 8.1. Suppressed kernels 61
• 8.2. From real-valued kernel to vector valued kernel 67
• 8.3. From one lattice to two lattices 68
• 8.4. Core suppression 69
• Chapter 9. The Third Reduction 71
• Chapter 10. The Fourth Reduction 73
• 10.1. [mu], b, D, [eta] decomposition 73
• 10.2. Good functions and bad functions 74
• 10.3. Estimates of nonhomogeneous Calderon-Zygmund operators on good functions 76
• 10.4. The reduction of Theorem 9.1 to estimates of nonhomogeneous Calderon-Zygmund operator, namely to Theorem 10.6 78
• Chapter 11. The Proof of Nonhomogeneous Cotlar's Lemma. Arbitrary Measure 83
• Chapter 12. Starting the Proof of Nonhomogeneous Nonaccretive Tb Theorem 93
• 12.1. Terminal and transit cubes 94
• 12.2. Projections [Lambda] and [Delta subscript Q] 96
• Chapter 13. Next Step in Theorem 10.6. Good and Bad Functions 101
• 13.1. Good functions and bad functions again 101
• 13.2. Reduction to estimates on good functions 102
• 13.3. Splitting [left angle bracket]T[open phi subscript good], [psi subscript good right angle bracket] to three sums 103
• 13.4. Three types of estimates of [function of] k(x,y)f(x)g(y)d[mu](x)d[mu](y) 104
• 13.5. Estimate of long range interaction sum [sigma subscript 2] 106
• 13.6. Short range interaction sum [sigma subscript 3]. Nonhomogeneous paraproducts 109
• Chapter 14. Estimate of the Diagonal Sum. Remainder in Theorem 3.3 121
• 14.1. Estimate of [Sigma subscript term] 123
• 14.2. Estimate of [Sigma subscript tr] 126
• Chapter 15. Two Weight Estimate for the Hilbert Transform. Preliminaries 127
• Chapter 16. Necessity in the Main Theorem 133
• Chapter 17. Two Weight Hilbert Transform. Towards the Main Theorem 135
• 17.1. Bad and good parts of f and g 136
• 17.2. Estimates on good functions 137
• Chapter 18. Long Range Interaction 139
• Chapter 19. The Rest of the Long Range Interaction 143
• Chapter 20. The Short Range Interaction 145
• 20.1. The estimate of neighbor-terms 145
• 20.2. The estimate of stopping terms 145
• 20.3. The choice of stopping intervals 147
• Chapter 21. Difficult Terms and Several Paraproducts 153
• 21.1. First paraproduct 154
• 21.2. Two more paraproducts 156
• 21.3. Second paraproduct: miraculous improvement of the Carleson property 159
• Chapter 22. Two-Weight Hilbert Transform and Maximal Operator 161
• 22.1. Doubling 161
• 22.2. No doubling 163.

Notes:

• "CBMS Regional Research Conference, Nonhomogeneous Harmonic Analysis, Weights, and Applications to Problems in Complex Analysis and Operator Theory, University of North Carolina, May 13-17, 2002"--t.p. verso.
• Includes bibliographical references.

ISBN:

0821832522

OCLC:

53276503