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Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction.......................................................................................................................................................... 5
Chapter I. Some preliminary lemmas............................................................................................................ 8
Chapter II. Weighted $H^p$ spaces of analytic functions.......................................................................... 13
1. Behaviour at the boundary....................................................................................................................... 13
2. Maximal function characterization........................................................................................................... 15
3. Atomic decomposition.............................................................................................................................. 20
4. Dual spaces............................................................................................................................................... 27
Chapter III. $H^p$ spaces associated with the space of homogeneous type (R, w(x)dx).................... 31
1. The space $\mathfrak{H}^1(w(x)dx)$...................................................................................................... 31
2. The spaces $\mathfrak{H}^p(w(x)dx)$ for p < 1.................................................................................... 33
Chapter IV. Applications and examples.......................................................................................................... 40
1. A weighted Hilbert transform.................................................................................................................... 40
2. Equivalence between the space of radial functions in $H^1(R^n)$ and the space
of even functions in $\mathfrak{H}^1(|r|^{n-1}dr)$..................................................................................... 40
3. Integral operators in the line obtained by restricting to radial functions some systems
of Riesz transforms in higher dimensions................................................................................................. 44
4. The kernel $z^{-2}$...................................................................................................................................... 54
References............................................................................................................................................................. 58
Introduction.......................................................................................................................................................... 5
Chapter I. Some preliminary lemmas............................................................................................................ 8
Chapter II. Weighted $H^p$ spaces of analytic functions.......................................................................... 13
1. Behaviour at the boundary....................................................................................................................... 13
2. Maximal function characterization........................................................................................................... 15
3. Atomic decomposition.............................................................................................................................. 20
4. Dual spaces............................................................................................................................................... 27
Chapter III. $H^p$ spaces associated with the space of homogeneous type (R, w(x)dx).................... 31
1. The space $\mathfrak{H}^1(w(x)dx)$...................................................................................................... 31
2. The spaces $\mathfrak{H}^p(w(x)dx)$ for p < 1.................................................................................... 33
Chapter IV. Applications and examples.......................................................................................................... 40
1. A weighted Hilbert transform.................................................................................................................... 40
2. Equivalence between the space of radial functions in $H^1(R^n)$ and the space
of even functions in $\mathfrak{H}^1(|r|^{n-1}dr)$..................................................................................... 40
3. Integral operators in the line obtained by restricting to radial functions some systems
of Riesz transforms in higher dimensions................................................................................................. 44
4. The kernel $z^{-2}$...................................................................................................................................... 54
References............................................................................................................................................................. 58
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
162
Liczba stron
58
Liczba rozdzia³ów
Opis fizyczny
1979
Daty
wydano
1979
Twórcy
autor
- Washington University, St. Louis, Missouri
- Universidad Complutense, Madrid, Spain
Bibliografia
- [1] R. R. Coifman, A real variable characterization of $H^p$, Studia Math. 51 (1974), p. 259-274.
- [2] R. R. Coifman, and C. Fefferman, Weighted norm, inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), p. 241-250.
- [3] R. R. Coifman and G. Weiss, Analyse harmonique non commutative sur certains espaces homogènes, Lecture notes in Mathematics 242, Springer-Verlag, Berlin 1971.
- [4] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. (to appear).
- [5] A. Erdelyi (director), Higher transcendental functions, Vol. I—III, Bateman Manuscript Project, McGraw-Hill, New York 1953.
- [6] A. Erdelyi (director), Tables of integral transforms, Vol. I—II, Bateman Manuscript Project, McGraw-Hill, New York 1954.
- [7] C. Fefferman, Harmonic analysis and $H^p$ spaces, in Studies in Harmonic Analysis (J. M. Ash, Editor), M.A.A.
- [8] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables. Acta Math. 129 (1972),p. 137-193.
- [9] A. Gandulfo, J. Garcia-Cuerva and M. Taibleson, Conjugate system characterizations of $H^l$: counterexamples for the euclidean plane and local fields, Bull. Amer. Math. Soc. Vol. 82, 1 (1976), p. 83-85.
- [10] R. A. Hunt, B. Muckenhoupt and R. L. Wheeden, Weighted norm inequalities for the conjugate function and the Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), p. 227-251.
- [11] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure App. Math. 14 (1961), p. 415-426.
- [12] R. Macias, Interpolation theorems on generalized Hardy spaces, Ph. D. dissertation, Washington University, St. Louis, Missouri 1974.
- [13] B. Muckenhoupt, Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), p. 207-226.
- [14] B. Muckenhoupt and E. M. Stein, Classical expansions and their relations to conjugate harmonic functions, Trans. Amer. Math. Soc. 118 (1965), p. 17-92.
- [15] B. Muckenhoupt and R. L. Wheeden, Weighted bounded mean oscillation and the Hilbert transform, Studia Math. 54 (1976), p. 221-237.
- [16] M. Rosenblum, Summability of Fourier series in $L^p${dμ), Trans. Amer. Math. Soc. 105, 1 (1962), p. 32-42.
- [17] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton 1970.
- [18] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton 1971.
- [19] K. Yosida, Functional analysis, Springer-Verlag, 1968.
Języki publikacji
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Identyfikator YADDA
bwmeta1.element.zamlynska-e75bca70-ae0a-4b42-b3cb-fc9e2b3cbad8
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ISSN
0012-3862
ISBN
83-01-01098-3
Kolekcja
DML-PL
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