Related papers: Cancellation for the simplex Hilbert transform

We prove $\mathrm{L}^p$ bounds for the truncated simplex Hilbert transform which grow with a power less than one of the truncation range in the logarithmic scale.

For any natural number $k$, consider the $k$-linear Hilbert transform $$ H_k( f_1,\dots,f_k )(x) := \operatorname{p.v.} \int_{\bf R} f_1(x+t) \dots f_k(x+kt)\ \frac{dt}{t}$$ for test functions $f_1,\dots,f_k: {\bf R} \to {\bf C}$. It is…

In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…

We study a multilinear singular integral obtained by taking averages of simplex Hilbert transforms. This multilinear form is also closely related to Calder\'on commutators and the twisted paraproduct. We prove $L^p$ bounds in dimensions two…

We derive a stronger uniqueness result if a function with compact support and its truncated Hilbert transform are known on the same interval by using the Sokhotski-Plemelj formulas. To find a function from its truncated Hilbert transform,…

This paper presents a solution to a problem from superanalysis about the existence of Hilbert-Banach superalgebras. Two main results are derived: 1) There exist Hilbert norms on some graded algebras (infinite-dimensional superalgebras…

An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.

A family of regularization functionals is said to admit a linear representer theorem if every member of the family admits minimizers that lie in a fixed finite dimensional subspace. A recent characterization states that a general class of…

We extend to multilinear Hankel operators the fact that some truncations of bounded Hankel operators are bounded. We prove and use a continuity property of bilinear Hilbert transforms on products of Lipschitz spaces and Hardy spaces.

This paper has been withdrawn since it contains some discrepancy with othe authers's recent result. We will not post this until this discrepancy is resolved.

In this paper, for $1<p<\infty$, we obtain the $L^p$-boundedness of the Hilbert transform $H^{\gamma}$ along a variable plane curve $(t,u(x_1, x_2)\gamma(t))$, where $u$ is a Lipschitz function with small Lipschitz norm, and $\gamma$ is a…

In this paper, we give a simple proof for the small cancellation conditions of the upper presentations of 2-bridge link groups, which holds the key to the proof of the main result of [1]. We also give an alternative proof of the main result…

We present new estimates for sums of the divisor function, and other similar arithmetic functions, in short intervals over function fields. (When the intervals are long, one obtains a good estimate from the Riemann hypothesis.) We obtain an…

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

We extend to multilinear Hankel operators the fact that truncation of bounded Hankel operators is bounded. We prove and use a continuity property of a kind of bilinear Hilbert transforms on product of Lipschitz spaces and Hardy spaces.

In the framework of abstract linear inverse problems in infinitedimensional Hilbert space we discuss generic convergence behaviours of approximate solutions determined by means of general projection methods, namely outside the standard…

The paper discusses a series of results concerning reproducing kernel Hilbert spaces, related to the factorization of their kernels. In particular, it is proved that for a large class of spaces isometric multipliers are trivial. One also…

We present direct numerical simulations and Lagrangian averaged (also known as alpha-model) simulations of forced and free decaying magnetohydrodynamic turbulence in two dimensions. The statistics of sign cancellations of the current at…

The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen's hypergeometric series with unit argument, when one numerator parameter and one denominator parameter are negative integers. Further,…

In this paper generalize Robinson's version of an order cancellation law for subsets of vector spaces in which we cancel by unbounded sets. We introduce the notion of weakly narrow sets in normed spaces, study their properties and prove the…