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Helical maximal function and weighted estimates

Abhishek Ghosh, Kalachand Shuin

Abstract

In this article, we characterize the range of $α$ for which the helical maximal function is bounded from $L^p(|x|^α)$ to itself for $3<p<\infty$. Our result is optimal for $4\leq p<\infty,$ except possibly at end-points.

Helical maximal function and weighted estimates

Abstract

In this article, we characterize the range of for which the helical maximal function is bounded from to itself for . Our result is optimal for except possibly at end-points.
Paper Structure (8 sections, 15 theorems, 102 equations)

This paper contains 8 sections, 15 theorems, 102 equations.

Table of Contents

  1. introduction
  2. Statement of main result
  3. Comparison with previously known results
  4. Necessary conditions
  5. Proof of main results
  6. Proof of Theorem \ref{['full']} for $4\leq p<\infty$
  7. Proof of Theorem \ref{['full']} for $3<p<4$
  8. Lacunary maximal function

Key Result

Theorem 1.1

Let $\gamma: I\to \mathbb{R}^3$ be a smooth non-degenerate curve, i.e., $\gamma$ satisfies nondegenerate.

Theorems & Definitions (30)

  • Theorem 1.1
  • Proposition 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Theorem 1.5: BeltranPLMS
  • Theorem 1.6
  • Proposition 1.7
  • Remark 1.8
  • proof : Proof of Proposition \ref{['comparison1']}
  • Proposition 1.9
  • ...and 20 more