Differentiation in lacunary directions
Proceedings of the National Academy of SciencesPublished 1 March 1978Open access
Alexander Nagel, E. M. Stein, Stephen Wainger
Citations136
SJR quartileQ1
SJR score3.41
SNIP2.38
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
Theta(j) is a lacunary sequence going to zero and it is proved that J = 0, where J is the number of particles in the LaSalle–Seiden inequality.
Abstract
Let {theta(j)} be a lacunary sequence going to zero. Let [Formula: see text]. Define [Formula: see text]. We prove [Formula: see text].
Keywords
Mathematics
Proceedings of the National Academy of SciencesOn the equivalence between the boundedness of certain classes of maximal and multiplier operators in Fourier analysis
61 Citations1977Antonio Córdoba, Robert Fefferman
The relationship between certain multipliers generalizing the Hilbert transform and maximal operatorsgeneralizing the Hardy-Littlewood maximal function is studied and some consequences of this relation are derived.
Proceedings of the National Academy of SciencesOn differentiation of integrals
50 Citations1977Antonio Córdoba, Robert Fefferman
It is found that the basis associated with a sparse set of directions differentiates integrals of functions locally in L(2) in order to relate differentiation and covering properties of a basis.
