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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
1. Introduction and main results...............................................................5
2. Preliminaries.......................................................................................12
3. The sampling theorem and polar wavelet identity...............................25
4. Boundedness of almost diagonal matrices on $a^{αq}_{p}$...............27
5. Peetre's maximal inequality.................................................................31
6. Norm characterizations.......................................................................35
7. FHT multiplier and potential operators................................................39
8. Equivalence of $L^p$ and $A^{02}_p$, 1 < p < ∞...............................42
9. Conclusion..........................................................................................49
References.............................................................................................50
1. Introduction and main results...............................................................5
2. Preliminaries.......................................................................................12
3. The sampling theorem and polar wavelet identity...............................25
4. Boundedness of almost diagonal matrices on $a^{αq}_{p}$...............27
5. Peetre's maximal inequality.................................................................31
6. Norm characterizations.......................................................................35
7. FHT multiplier and potential operators................................................39
8. Equivalence of $L^p$ and $A^{02}_p$, 1 < p < ∞...............................42
9. Conclusion..........................................................................................49
References.............................................................................................50
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
348
Liczba stron
51
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXLVIII
Daty
wydano
1996
otrzymano
1995-03-02
Twórcy
autor
- Department of Mathematics, University of New Mexico, Albuquerque, New Mexico 87131, U.S.A.
autor
- Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, U.S.A.
Bibliografia
- [BaF] G. Battle and P. Federbush, Divergence-free vector wavelets, Michigan Math. J. 40 (1993), 181-195.
- [BF] J. Benedetto and M. Frazier (eds.), Wavelets: Mathematics and Applications, CRC Press, Boca Raton, Fla., 1993.
- [CZ] A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139.
- [CF] S.-Y. A. Chang and R. Fefferman, Some recent developments in Fourier analysis and $H^p$-theory on product domains, Bull. Amer. Math. Soc. 12 (1985), 1-43.
- [Ch] C. K. Chui (ed.), Wavelets: A Tutorial in Theory and Applications, Academic Press, New York, 1992.
- [D1] I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), 909-996.
- [D2] I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. Appl. Math. 61, SIAM, Philadelphia, Penn., 1992.
- [DJ] G. David and J.-L. Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. 120 (1984), 371-397.
- [E] R. E. Edwards, Functional Analysis, Holt, Rinehart and Winston, New York, 1965.
- [EF] J. Epperson and M. Frazier, An almost orthogonal radial wavelet expansion for radial distributions, J. Fourier Anal. Appl. 1 (1995), 311-353.
- [F] P. Federbush, Navier and Stokes meet the wavelet, Comm. Math. Phys. 155 (1993), 219-248.
- [FS] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1972), 107-115.
- [Fo] G. B. Folland, Lectures on Partial Differential Equations, Tata Institute of Fundamental Research, Bombay, Springer, New York, 1983.
- [FJ1] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799.
- [FJ2] M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Function Spaces and Applications, M. Cwikel et al. (eds.), Lecture Notes in Math. 1302, Springer, Berlin, 1988, 223-246.
- [FJ3] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
- [FJ4] M. Frazier and B. Jawerth, Applications of the φ and wavelet transforms to the theory of function spaces, in: Wavelets and Their Applications, M. Ruskai et al. (eds.), Jones and Bartlett, Boston, 1992, 377-417.
- [FJW] M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conf. Ser. in Math. 79, Amer. Math. Soc., Providence, R.I., 1991.
- [H] J. R. Higgins, Five short stories about the cardinal series, Bull. Amer. Math. Soc. 12 (1985), 45-89.
- [JT] B. Jawerth and A. Torchinsky, Local sharp maximal functions, J. Approx. Theory 43 (1985), 231-270.
- [Ma] S. Mallat, Multiresolution approximations and wavelet orthonormal bases of L²(ℝ), Trans. Amer. Math. Soc. 315 (1989), 69-87.
- [M1] Y. Meyer, Principe d'incertitude, bases Hilbertiennes et algèbres d'opérateurs, Séminaire Bourbaki 662 (1985-1986), 1-15.
- [M2] Y. Meyer, Ondelettes et Opérateurs, Hermann, Paris, 1990.
- [M3] Y. Meyer, Ondelettes sur l'intervalle, Rev. Mat. Iberoamericana 7 (1991), 115-133.
- [P] J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123-130.
- [R] M. Ruskai, G. Beylkin, R. Coifman, I. Daubechies, S. Mallat, Y. Meyer and L. Raphael (eds.), Wavelets and Their Applications, Jones and Bartlett, Boston, 1992.
- [Se-S] A. Seeger and C. D. Sogge, On the boundedness of functions of (pseudo-) differential operators on compact manifolds, Duke Math. J. 59 (1989), 709-736.
- [S1] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
- [S2] E. M. Stein, Harmonic Analysis, Princeton Univ. Press, Princeton, N.J., 1993.
- [SW] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.
- [Str] R. S. Strichartz, Construction of orthonormal wavelets, in: Wavelets: Mathematics and Applications, J. Benedetto and M. Frazier (eds.), CRC Press, Boca Raton, Fla., 1993, 23-50.
- [T1] H. Triebel, Theory of Function Spaces, Monographs Math. 78, Birkhäuser, Basel, 1983.
- [T2] H. Triebel, Theory of Function Spaces II, Monographs Math. 84, Birkhäuser, Basel, 1992.
- [W] G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, 1944.
Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 42B25, 42C15.
Identyfikator YADDA
bwmeta1.element.zamlynska-12704ab5-a4b6-465a-b97f-abc32ee460f9
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki
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