## One Citation

### Uniform $L^p$ estimates for the Hilbert transform and maximal operator along a new class of variable curves

- Mathematics
- 2022

We investigate the linear Hilbert transform and maximal operator along a new class of variable non-flat polynomial curves and prove uniform L-boundedness for 1 < p < ∞. The uniform is in a sense that…

## References

SHOWING 1-10 OF 43 REFERENCES

### Hilbert transform along measurable vector fields constant on Lipschitz curves : L2 boundedness

- Mathematics
- 2014

We prove the $L^p (p > 3/2)$ boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.

### Hilbert transform along measurable vector fields constant on Lipschitz curves: $L^p$ boundedness

- Mathematics
- 2014

We prove the $L^p (p > 3/2)$ boundedness of the directional Hilbert transform in the plane relative to measurable vector fields which are constant on suitable Lipschitz curves.

### Maximal functions and Hilbert Transforms along variable flat curves

- Mathematics
- 1999

In this work we establish Lp boundedness for maximal functions and Hilbert transforms along variable curves in the plane, via L2 estimates for certain singular integral operators with oscillatory…

### Hilbert transforms and maximal functions along variable flat curves

- Mathematics
- 2002

We study certain Hilbert transforms and maximal functions along variable flat curves in the plane. We obtain their L 2 (R 2 ) boundedness by considering the oscillatory singular integrals which arise…

### Maximal operators and Hilbert transforms along variable non‐flat homogeneous curves

- Mathematics
- 2016

We prove that the maximal operator associated with variable homogeneous planar curves (t,utα)t∈R , α≠1 positive, is bounded on Lp(R2) for each p>1 , under the assumption that u:R2→R is a Lipschitz…

### Square functions for bi-Lipschitz maps and directional operators

- MathematicsJournal of Functional Analysis
- 2018

### Singular Radon transforms and maximal functions under convexity assumptions

- Mathematics
- 2002

We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal functions along convex curves in the plane.

### Lp estimates for the Hilbert transforms along a one-variable vector field

- Mathematics
- 2013

Stein conjectured that the Hilbert transform in the direction of a vector field is bounded on, say, $L^2$ whenever $v$ is Lipschitz. We establish a wide range of $L^p$ estimates for this operator…

### Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces

- Mathematics
- 2011

AbstractA new moment inequality is obtained for the eigenfunctions ϕ of the flat tours Πn. More specifically, it is known that the
$p = \frac{{2n}}
{{n - 1}}
$
is almost uniformaly bounded.…

### Local smoothing of Fourier integral operators and Carleson-Sjölin estimates

- Mathematics
- 1993

The purpose of this paper is twofold. First, if Y and Z are smooth paracompact manifolds of dimensions n ~ 2 and n + 1 , respectively, we shall prove local regularity theorems for a certain class of…