Endpoint Sobolev Regularity of Multilinear Maximal Operators

Multilinear Fourier Multipliers with Minimal Sobolev Regularity

Letm be a positive integer. In this talk, we will introduce optimal conditions,expressed in terms of Sobolev spaces, on m-linear Fourier multiplier operatorsto be bounded from a product of Lebesgue or Hardy spaces to Lebesgue spaces.Our results are sharp and cover the bilinear case (m = 2) obtained by Miyachiand Tomita [1]. References[1] Miyachi A., and Tomita N., Minima...

Multilinear Fourier Multipliers with Minimal Sobolev Regularity, I

We find optimal conditions on m-linear Fourier multipliers to give rise to bounded operators from a product of Hardy spaces Hj , 0 < pj ≤ 1, to Lebesgue spaces Lp. The conditions we obtain are necessary and sufficient for boundedness and are expressed in terms of L2-based Sobolev spaces. Our results extend those obtained in the linear case (m = 1) by Calderón and Torchinsky [1] and in the bilin...

On the Regularity of Maximal Operators

We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W (R) × W (R) → W (R) with 1 < p, q < ∞ and r ≥ 1, boundedly and continuously. The same result holds on R when r > 1. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versi...

Elliptic operators and maximal regularity on periodic little-Hölder spaces

Some Estimates for Rough Multilinear Fractional Integral Operators and Rough Multi-sublinear Fractional Maximal Operators

It is well known that, for the purpose of researching non-smoothness partial differential equation, mathematicians pay more attention to the singular integrals with rough kernel. Moreover, the fractional type operators and their weighted boundedness theory play important roles in harmonic analysis and other fields, and the multilinear operators arise in numerous situations involving product-lik...