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Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets
1. | University of Missouri, Columbia, MO 65211, United States, United States, United States, United States |
References:
[1] |
P. Auscher, Lectures on the Kato square root problem,, in Surveys in Analysis and Operator Theory (Canberra, (2001), 1.
|
[2] |
P. Auscher, S. Hofmann, M. Lacey, A. McIntosh and P. Tchamitchian, The solution of the Kato square root problem for second order elliptic operators on $\mathbbR^n$,, Annals of Math. (2), 156 (2002), 633.
doi: 10.2307/3597201. |
[3] |
J. Azzam and R. Schul, Hard Sard: Quantitative implicit function and extension theorems for Lipschitz maps,, Geom. Funct. Anal., 22 (2012), 1062.
doi: 10.1007/s00039-012-0189-0. |
[4] |
D. Brigham, D. Mitrea, I. Mitrea and M. Mitrea, Triebel-Lizorkin sequence spaces are genuine mixed-norm spaces,, Math. Nachr., 286 (2013), 503.
doi: 10.1002/mana.201100184. |
[5] |
M. Christ, A $T(b)$ theorem with remarks on analytic capacity and the Cauchy integral,, Colloq. Math., 60/61 (1990), 601.
|
[6] |
R. R. Coifman, A. McIntosh and Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes,, Ann. of Math. (2), 116 (1982), 361.
doi: 10.2307/2007065. |
[7] |
R. Coifman, Y. Meyer and E. M. Stein, Some new function spaces and their applications to harmonic analysis,, J. Funct. Anal., 62 (1985), 304.
doi: 10.1016/0022-1236(85)90007-2. |
[8] |
R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis,, Bull. Amer. Math. Soc., 83 (1977), 569.
doi: 10.1090/S0002-9904-1977-14325-5. |
[9] |
G. David, Morceaux de graphes lipschitziens et intégrales singulières sur une surface,, Rev. Mat. Iberoamericana, 4 (1988), 73.
doi: 10.4171/RMI/64. |
[10] |
G. David and S. Semmes, Singular integrals and rectifiable sets in $\mathbbR^n$: Beyond Lipschitz graphs,, Astérisque, 193 (1991).
|
[11] |
G. David and S. Semmes, Analysis of and on Uniformly Rectifiable Sets,, Mathematical Surveys and Monographs, (1993).
|
[12] |
S. Hofmann, Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials,, Duke Math. J., 90 (1997), 209.
doi: 10.1215/S0012-7094-97-09008-6. |
[13] |
S. Hofmann, Local $Tb$ Theorems and applications in PDE,, in International Congress of Mathematicians, (2006), 1375.
|
[14] |
S. Hofmann, M. Lacey and A. McIntosh, The solution of the Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds,, Annals of Math. (2), 156 (2002), 623.
doi: 10.2307/3597200. |
[15] |
S. Hofmann and J. L. Lewis, Square functions of Calderón type and applications,, Rev. Mat. Iberoamericana, 17 (2001), 1.
doi: 10.4171/RMI/287. |
[16] |
S. Hofmann and A. McIntosh, The solution of the Kato problem in two dimensions,, in Proceedings of the Conference on Harmonic Analysis and PDE (El Escorial, (2000), 143.
doi: 10.5565/PUBLMAT_Esco02_06. |
[17] |
S. Hofmann and A. McIntosh, Boundedness and applications of singular integrals and square functions: A survey,, Bull. Math. Sci., 1 (2011), 201.
doi: 10.1007/s13373-011-0014-3. |
[18] |
R. A. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type,, Adv. in Math., 33 (1979), 257.
doi: 10.1016/0001-8708(79)90012-4. |
[19] |
R. A. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type,, Adv. in Math., 33 (1979), 271.
doi: 10.1016/0001-8708(79)90013-6. |
[20] |
D. Mitrea, I. Mitrea and M. Mitrea, Weighted mixed-normed spaces on spaces of homogeneous type,, preprint, (2012). Google Scholar |
[21] |
D. Mitrea, I. Mitrea, M. Mitrea and S. Monniaux, Groupoid Metrization Theory. With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis,, Applied and Numerical Harmonic Analysis, (2013).
doi: 10.1007/978-0-8176-8397-9. |
show all references
References:
[1] |
P. Auscher, Lectures on the Kato square root problem,, in Surveys in Analysis and Operator Theory (Canberra, (2001), 1.
|
[2] |
P. Auscher, S. Hofmann, M. Lacey, A. McIntosh and P. Tchamitchian, The solution of the Kato square root problem for second order elliptic operators on $\mathbbR^n$,, Annals of Math. (2), 156 (2002), 633.
doi: 10.2307/3597201. |
[3] |
J. Azzam and R. Schul, Hard Sard: Quantitative implicit function and extension theorems for Lipschitz maps,, Geom. Funct. Anal., 22 (2012), 1062.
doi: 10.1007/s00039-012-0189-0. |
[4] |
D. Brigham, D. Mitrea, I. Mitrea and M. Mitrea, Triebel-Lizorkin sequence spaces are genuine mixed-norm spaces,, Math. Nachr., 286 (2013), 503.
doi: 10.1002/mana.201100184. |
[5] |
M. Christ, A $T(b)$ theorem with remarks on analytic capacity and the Cauchy integral,, Colloq. Math., 60/61 (1990), 601.
|
[6] |
R. R. Coifman, A. McIntosh and Y. Meyer, L'intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes,, Ann. of Math. (2), 116 (1982), 361.
doi: 10.2307/2007065. |
[7] |
R. Coifman, Y. Meyer and E. M. Stein, Some new function spaces and their applications to harmonic analysis,, J. Funct. Anal., 62 (1985), 304.
doi: 10.1016/0022-1236(85)90007-2. |
[8] |
R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis,, Bull. Amer. Math. Soc., 83 (1977), 569.
doi: 10.1090/S0002-9904-1977-14325-5. |
[9] |
G. David, Morceaux de graphes lipschitziens et intégrales singulières sur une surface,, Rev. Mat. Iberoamericana, 4 (1988), 73.
doi: 10.4171/RMI/64. |
[10] |
G. David and S. Semmes, Singular integrals and rectifiable sets in $\mathbbR^n$: Beyond Lipschitz graphs,, Astérisque, 193 (1991).
|
[11] |
G. David and S. Semmes, Analysis of and on Uniformly Rectifiable Sets,, Mathematical Surveys and Monographs, (1993).
|
[12] |
S. Hofmann, Parabolic singular integrals of Calderón-type, rough operators, and caloric layer potentials,, Duke Math. J., 90 (1997), 209.
doi: 10.1215/S0012-7094-97-09008-6. |
[13] |
S. Hofmann, Local $Tb$ Theorems and applications in PDE,, in International Congress of Mathematicians, (2006), 1375.
|
[14] |
S. Hofmann, M. Lacey and A. McIntosh, The solution of the Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds,, Annals of Math. (2), 156 (2002), 623.
doi: 10.2307/3597200. |
[15] |
S. Hofmann and J. L. Lewis, Square functions of Calderón type and applications,, Rev. Mat. Iberoamericana, 17 (2001), 1.
doi: 10.4171/RMI/287. |
[16] |
S. Hofmann and A. McIntosh, The solution of the Kato problem in two dimensions,, in Proceedings of the Conference on Harmonic Analysis and PDE (El Escorial, (2000), 143.
doi: 10.5565/PUBLMAT_Esco02_06. |
[17] |
S. Hofmann and A. McIntosh, Boundedness and applications of singular integrals and square functions: A survey,, Bull. Math. Sci., 1 (2011), 201.
doi: 10.1007/s13373-011-0014-3. |
[18] |
R. A. Macías and C. Segovia, Lipschitz functions on spaces of homogeneous type,, Adv. in Math., 33 (1979), 257.
doi: 10.1016/0001-8708(79)90012-4. |
[19] |
R. A. Macías and C. Segovia, A decomposition into atoms of distributions on spaces of homogeneous type,, Adv. in Math., 33 (1979), 271.
doi: 10.1016/0001-8708(79)90013-6. |
[20] |
D. Mitrea, I. Mitrea and M. Mitrea, Weighted mixed-normed spaces on spaces of homogeneous type,, preprint, (2012). Google Scholar |
[21] |
D. Mitrea, I. Mitrea, M. Mitrea and S. Monniaux, Groupoid Metrization Theory. With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis,, Applied and Numerical Harmonic Analysis, (2013).
doi: 10.1007/978-0-8176-8397-9. |
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