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 associated to smooth curves.

E M Stein1, S Wainger

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

Proceedings of the National Academy of Sciences of the United States of America
|December 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

In This Issue.

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

Long-term cultural continuity across the Neanderthal-modern human sequence at Üçağızlı II Cave, northern Levant.

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

Dolphins use names to remember whom to avoid.

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

Retraction for Shaked and Frenkel, Curiouser and curiouser: Meningeal lymphoid structures in the aging brain.

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

Small but mighty: The outsized role of small water bodies in the global carbon cycle.

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

Functional traits produce conditional outcomes in different community contexts.

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

This study analyzes a maximal function defined using a smooth curve. It establishes conditions for boundedness of this function in L(p) spaces, crucial for harmonic analysis.

Area of Science:

  • Harmonic Analysis
  • Functional Analysis
  • Real Analysis

Background:

  • Maximal functions are fundamental operators in harmonic analysis.
  • The study of boundedness properties of these operators is a key area of research.
  • Previous work has focused on various types of maximal operators, but the specific case involving smooth curves requires detailed investigation.

Purpose of the Study:

  • To define and analyze a novel maximal function based on a smooth curve in n-dimensional Euclidean space (IRn).
  • To establish the L(p) boundedness of this maximal function, which is essential for understanding its analytical properties.
  • To determine the precise conditions on the curve gamma(t) that ensure the boundedness of the maximal function.

Main Methods:

  • Definition of the maximal function using a supremum over scales (h) and an integral along the curve gamma(t).

Related Experiment Videos

  • Application of techniques from real and functional analysis to derive boundedness estimates.
  • Investigation of the properties of the smooth curve gamma(t) to control the integral term.

    • Main Results:

    • The study states conditions under which the maximal function is bounded in L(p) spaces for 1 < p <= infinity.
    • An inequality of the form ||[unk](f)||(p) <= A(p) ||f||(p) is established, where A(p) is a constant depending on p.
    • These results contribute to the understanding of the analytical behavior of integral operators with variable kernels.

    Conclusions:

    • The boundedness of the defined maximal function is proven under specific conditions related to the underlying smooth curve.
    • The findings have implications for the theory of integral operators and their applications in mathematical analysis.
    • This work extends the existing literature on maximal functions by considering a more general class of curves.