4 citations · 8 across the 5 of their papers we have counts for
8 papers
Multilinear rough singular integral operators may not be of the weak type at the endpoint
Petr Honzik
We show that -linear homogeneous rough singular integral operators $\LL_Ω$ associated with functions on with mean value zero may not be bounde…
On pointwise a.e. convergence of multilinear operators
Loukas Grafakos, Danqing He, Petr Honzík +1
In this work we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) truncated homogeneous singular integral operators associated with…
Initial bounds for multilinear operators
Loukas Grafakos, Danqing He, Petr Honzík +1
The boundedness theory of convolution operators is \linebreak based on an initial estimate derived from the Fourier transform. The corresponding theory of multil…
Maximal operators associated with bilinear multipliers of limited decay
Loukas Grafakos, Danqing He, Petr Honzík
Results analogous to those proved by Rubio de Francia are obtained for a class of maximal functions formed by dilations of bilinear multiplier operators of limited decay. We focus…
Bilinear Spherical Maximal Function
J. A. Barrionevo, Loukas Grafakos, Danqing He +2
We obtain boundedness for the bilinear spherical maximal function in a range of exponents that includes the Banach triangle and a range of with . We also obtain countere…
The Hörmander multiplier theorem I: The Linear Case
Loukas Grafakos, Danqing He, Petr Honzík +1
We discuss boundedness for Fourier multiplier operators that satisfy the hypotheses of the Hörmander multiplier theorem in terms of an optimal condition that rel…
Rough Bilinear Singular Integrals
Loukas Grafakos, Danqing He, Petr Honzík
We study the rough bilinear singular integral, introduced by Coifman and Meyer , $$ T_Ω(f,g)(x)=p.v. \! \int_{\mathbb R^{n}}\! \int_{\mathbb R^{n}}\! |(y,z)|^{-2n} Ω((y,z)/|(y,z)|)…
On the Good- inequality for nonlinear potentials
Petr Honzík, Benjamin J. Jaye
This note concerns an extension of the good- inequality for fractional integrals, due to B. Muckenhoupt and R. Wheeden. The classical result is refined in two aspects. Firstly,…