Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Maximal functions: Spherical means.

E M Stein1

  • 1Department of Mathematics, Princeton University, Princeton, New Jersey 08540.

Proceedings of the National Academy of Sciences of the United States of America
|July 1, 1976
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The skeletal consequences of epidural steroid injections: a literature review.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2021
Same author

Risk factors for multi-joint disease in patients with glucocorticoid-induced osteonecrosis.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2021
Same author

Low volumetric bone density is a risk factor for early complications after spine fusion surgery.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2020
Same author

Disrupted radial and tibial microarchitecture in patients with monoclonal gammopathy of undetermined significance.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2018
Same author

Abnormal microarchitecture and stiffness in postmenopausal women using chronic inhaled glucocorticoids.

Osteoporosis international : a journal established as result of cooperation between the European Foundation for Osteoporosis and the National Osteoporosis Foundation of the USA·2018
Same author

What is the clinical significance of esophagogastric junction outflow obstruction? evaluation of 60 patients at a tertiary referral center.

Neurogastroenterology and motility·2017
Same journal

Chemotactic self-organization captures the dynamics of mammalian hair follicle patterning.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Tomographic imaging of superconducting order using particle-hole interference.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inhibitory potential of autologous neutralizing antibodies sets quantitative limits on the rebound-competent HIV-1 reservoir.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Inferring epidemiological parameters under an infectious phylogeography model with visitor dynamics.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Analytical modeling for suction cup designs for skin-interfaced wearable devices.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Improving cell-free metabolism through direct integration of artificial respiratory chains.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

This study shows that the supremum of averages of functions over spheres is bounded for certain function spaces. This finding is relevant for harmonic analysis and partial differential equations.

Area of Science:

  • Harmonic Analysis
  • Real Analysis
  • Geometric Measure Theory

Background:

  • The study of averages of functions over geometric shapes is a fundamental concept in analysis.
  • Understanding the boundedness of integral operators is crucial for solving differential equations and in Fourier analysis.

Purpose of the Study:

  • To investigate the boundedness properties of a specific integral operator defined using spherical averages.
  • To determine the conditions on the function space and dimension for which this operator is bounded.

Main Methods:

  • The research utilizes techniques from real analysis and harmonic analysis.
  • The core of the method involves analyzing the behavior of the spherical maximal function operator.

Main Results:

Related Experiment Videos

  • The study establishes that the spherical maximal function operator is bounded on L^p(R^n) spaces.
  • The boundedness holds for p strictly greater than n/(n-1) and for dimensions n greater than or equal to 3.

Conclusions:

  • The findings provide precise conditions for the boundedness of the spherical maximal function, contributing to the understanding of integral operators in Euclidean spaces.
  • This result has implications for the regularity of solutions to certain partial differential equations and in the study of Fourier multipliers.