Access the full text.
Sign up today, get DeepDyve free for 14 days.
C. Moore, Xiaojing Zhang (2012)
A law of the iterated logarithm for general lacunary seriesColloquium Mathematicum, 126
J. Cooper (1973)
SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONSBulletin of The London Mathematical Society, 5
Santosh Ghimire, C. Moore (2014)
A lower bound in the tail law of the iterated logarithm for lacunary trigonometric series, 142
(1959)
� E exp f k − f N − 1 2 (S(f n )) 2 dx ≤ C ?
A Zygmund (1959)
Trigonometric Series
M. Weiss (1959)
The law of the iterated logarithm for lacunary trigonometric series.Transactions of the American Mathematical Society, 91
R. Bañuelos, I. Klemeš, C. Moore (1990)
The lower bound in the law of the iterated logarithm for harmonic functionsDuke Mathematical Journal, 60
R. Bañuelos, I. Klemeš, C. Moore (1988)
An analogue for harmonic functions of Kolmogorov’s law of the iterated logarithmDuke Mathematical Journal, 57
(1959)
Trigonometric Series. Cambridge: Cambridge University Press. �E exp ( fk − fN − 1 2 (S(fn)) 2 ) dx ≤ C
CN Moore (2007)
Random walksRamanujan Mathematical Society Mathematics Newsletter, 17
R. Salem, A. Zygmund (1932)
On Lacunary Trigonometric Series.Proceedings of the National Academy of Sciences of the United States of America, 33 11
R. Bañuelos, C. Moore (1999)
Probabilistic behavior of harmonic functions
S. Chang, J. Wilson, T. Wolfi (1985)
Some weighted norm inequalities concerning the schrödinger operatorsCommentarii Mathematici Helvetici, 60
(1950)
La loi du logarithme itéré pour les series trigonométriques lacunaire
C N Moore, X Zhang (2014)
A lower bound in the law of the iterated logarithm for general lacunary series, with Zhang, X.Studia Mathematica, 222
R. Jewett, K. Ross (1988)
Random Walks on ℤCollege Mathematics Journal, 19
C. Moore, Xiaojing Zhang (2014)
A lower bound in the law of the iterated logarithm for general lacunary seriesStudia Mathematica, 222
Shigeru Takahashi (1963)
THE LAW OF THE ITERATED LOGARITHM FOR A GAP SEQUENCE WITH INFINITE GAPSTohoku Mathematical Journal, 15
We will discuss subgaussian estimates in harmonic analysis involving the non-tangential maximal function $$N_{\alpha }f$$ N α f and the area function $$A_{\beta } f$$ A β f of a function f on $${\mathbb {R}}^n.$$ R n . We will first introduce subgaussian estimates in the setting of martingales; these then lead to analogous estimates for harmonic functions. Among the consequences of these are sharp $$L^p$$ L p inequalities $$\Vert N_{\alpha }f\Vert _p \le C_p \Vert A_{\beta }f\Vert _p$$ ‖ N α f ‖ p ≤ C p ‖ A β f ‖ p ; here $$C_p= O(\sqrt{p})$$ C p = O ( p ) as $$p \rightarrow \infty $$ p → ∞ and this order is sharp. The subgaussian estimates produce Laws of the Iterated Logarithm (LILs) involving the non-tangential maximal function and area function. These ideas are also applied to lacunary series of more general functions to yield LILs.
The Journal of Analysis – Springer Journals
Published: Nov 9, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.