Wavelet decomposition of harmonic functions in growth spaces

Kjersti Solberg Eikrem, Eugenia Malinnikova, Pavel Mozolyako

Type: Preprint

Publication Date: 2012-03-23

Citations: 3

Abstract

Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of harmonic functions along vertical lines.

Locations

arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Wavelet characterization of growth spaces of harmonic functions	2014	Kjersti Solberg Eikrem Eugenia Malinnikova Pavel Mozolyako
+	Growth Estimates for a Class of Subharmonic Functions in the Upper-half Space	2011	Lei Qiao
+	Characterization and boundary behavior of harmonic functions in growth spaces	2013	Kjersti Solberg Eikrem
+	Multiresolution Analysis on the Hardy Space of Analytic Functions	2010	A. Abdollahi Ebrahim Rahimi
+	On the Density Condition of a Multiresolution Analysis in Lebesgue Spaces	2017	Á. San Antolín
+	Finite orthogonal transforms and multiresolution analyses on intervals	1997	W. R. Madych
+	Stability in periodic multi-wavelet decompositions and recovery of functions	2005	Đinh Dũng
+	Growth Estimates for a Class of Subharmonic Functions in a Half Space	2008	Guoshuang Pan Guantie Deng
+	Characterization of multiplier spaces by wavelets and logarithmic Morrey spaces	2012	Qixiang Yang Yueping Zhu
+	Wavelet decomposition of the space of discrete periodic splines	2000	V. A. Kirushev V. N. Malozemov А. Б. Певный
+	Growth Estimates for a Class of Subharmonic Functions in a Half Plane	2008	Guoshuang Pan Guantie Deng
+	Construction of Multiresolution Analysis Based on Localized Reproducing Kernels	2017	Krzysztof Jan Nowak Margit Pap
+	Fourier Analysis, Multiresolution Analysis and Dilation Equations	1998	David Malone
+	A Construction of Rational Wavelets and Frames in Hardy--Sobolev Spaces With Applications to System Modeling	1998	Nicholas F. Dudley Ward J. R. Partington
+	Hyperbolic Wavelets and Multiresolution in the Hardy Space of the Upper Half Plane	2012	Hans G. Feichtinger Margit Pap
+ PDF Chat	A characterization of wavelet convergence in sobolev spaces	2001	Mark Kon Louise Arakellan Rapha
+	Wavelet characterization of weighted spaces (Harmonic Analysis and Nonlinear Partial Differential Equations)	2010	Kazuya Tachizawa
+	Wavelet characterization of weighted spaces (Harmonic Analysis and Nonlinear Partial Differential Equations)	2010	一哉立澤
+	<title>Multiresolution analysis on nonsmooth sets with applications</title>	1995	Björn Jawerth Gunnar Peters
+ PDF Chat	Multiresolution Analysis for Markov Interval Maps	2012	Jana Bohnstengel Marc Keßeböhmer

Works That Cite This (3)

Action	Title	Year	Authors
+ PDF Chat	Coefficients Multipliers of Weighted Spaces of Harmonic Functions	2015	Kjersti Solberg Eikrem Eugenia Malinnikova
+	Oscillation of H\"older Continuous Functions	2013	José G. Llorente Artur Nicolau
+ PDF Chat	Boundary oscillations of harmonic functions in Lipschitz domains	2016	Pavel Mozolyako

Works Cited by This (22)

Action	Title	Year	Authors
+	None	1998	José G. Llorente
+	On the radial variation of bounded analytic functions on the disc	1993	Jean Bourgain
+	Bounded projections, duality, and multipliers in spaces of harmonic functions.	1978	David L. Williams Allen Shields
+	The Classical Banach Spaces	2000	Joram Lindenstrauss Lior Tzafriri
+	An analogue for harmonic functions of Kolmogorov’s law of the iterated logarithm	1988	Rodrigo Bañuelos Ivo Klemeš Charles N. Moore
+ PDF Chat	Coefficients of Bloch and Lipschitz functions	1981	Grahame Bennett David A. Stegenga Richard M. Timoney
+ PDF Chat	An approximation property of harmonic functions in Lipschitz domains and some of its consequences	2003	Jorge Rivera-Noriega
+ PDF Chat	Vertical variation of harmonic functions in upper half-spaces	2001	Michael D. O’Neill
+	An extension of the Nevanlinna theory	1975	Boris Korenblum
+	On the Distortion of Boundary Sets Under Conformal Mappings	1985	Nikolai Makarov