Search Results - "Grafakos, Loukas"

An improvement of the Marcinkiewicz multiplier theorem by Grafakos, Loukas

“…We provide an improvement of the Marcinkiewicz multiplier theorem on ℝ n by relaxing the integrability hypothesis on the multiplier. In particular, when r > 1…”
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Some Remarks on the Mikhlin–Hörmander and Marcinkiewicz Multiplier Theorems: A Short Historical Account and a Recent Improvement by Grafakos, Loukas

“…We present a short historical overview of the Mikhlin–Hörmander and Marcinkiewicz multiplier theorems. We discuss different versions of them and provide…”
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On Sharp Olsen’s and Trace Inequalities for Multilinear Fractional Integrals by Grafakos, Loukas, Meskhi, Alexander

“…We establish a sharp Olsen type inequality g I α ( f 1 , … , f m ) L r q ≤ C g L ℓ q ∏ j = 1 m f j L s j p j for multilinear fractional integrals I α ( f → ) (…”
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The Bourgain–Brezis–Mironescu formula on ball Banach function spaces by Dai, Feng, Grafakos, Loukas, Pan, Zhulei, Yang, Dachun, Yuan, Wen, Zhang, Yangyang

“…Let p ∈ [ 1 , ∞ ) and X be a ball Banach function space on R n with an absolutely continuous norm for which the Hardy–Littlewood maximal operator is bounded on…”
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Sharp Inequalities for Linear Combinations of Orthogonal Martingales by Ding, Yong, Grafakos Loukas, Zhu, Kai

“…For any two real-valued continuous-path martingales X = {Xt}t≥0 and Y = {Yt}t≥0, with X and Y being orthogonal and Y being differentially subordinate to X, we…”
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Maximal operators associated with bilinear multipliers of limited decay by Grafakos, Loukas, He, Danqing, Honzík, Petr

“…Results analogous to those proved by Rubio de Francia [28] are obtained for a class of maximal functions formed by dilations of bilinear multiplier operators…”
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The multilinear Hörmander multiplier theorem with a Lorentz–Sobolev condition by Grafakos, Loukas, Park, Bae Jun

“…In this article, we provide a multilinear version of the Hörmander multiplier theorem with a Lorentz–Sobolev space condition. The work is motivated by the…”
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Sparse Domination and Weighted Estimates for Rough Bilinear Singular Integrals by Grafakos, Loukas, Wang, Zhidan, Xue, Qingying

“…Let r > 4 3 and let Ω ∈ L r ( S 2 n - 1 ) have vanishing integral. We show that the bilinear rough singular integral T Ω ( f , g ) ( x ) = p.v. ∫ R n ∫ R n Ω (…”
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On Fourier Transforms of Radial Functions and Distributions by Grafakos, Loukas, Teschl, Gerald

“…We find a formula that relates the Fourier transform of a radial function on  R n with the Fourier transform of the same function defined on R n +2 . This…”
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L^2\times L^2 \rightarrow L^1$$L2×L2→L1 boundedness criteria by Grafakos, Loukas, He, Danqing, Slavíková, Lenka

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L2×L2→L1 boundedness criteria by Grafakos, Loukas, He, Danqing, Slavíková, Lenka

“…We obtain a sharp L 2 × L 2 → L 1 boundedness criterion for a class of bilinear operators associated with a multiplier given by a signed sum of dyadic…”
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Multilinear operators with non-smooth kernels and commutators of singular integrals by DUONG, XUAN THINH, GRAFAKOS, LOUKAS, YAN, LIXIN

“…We obtain endpoint estimates for multilinear singular integral operators whose kernels satisfy regularity conditions significantly weaker than those of the…”
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The Hörmander multiplier theorem, II: The bilinear local $$L^2$$ L 2 case by Grafakos, Loukas, He, Danqing, Honzík, Petr

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VECTOR-VALUED SINGULAR INTEGRALS AND MAXIMAL FUNCTIONS ON SPACES OF HOMOGENEOUS TYPE by GRAFAKOS, LOUKAS, LIU, LIGUANG, YANG, DACHUN

“…The Fefferman-Stein vector-valued maximal function inequality is proved for spaces of homogeneous type. The approach taken here is based on the theory of…”
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The Kato-Ponce Inequality by Grafakos, Loukas, Oh, Seungly

“…In this article we revisit the inequalities of Kato and Ponce concerning the L r norm of the Bessel potential J s  = (1 − Δ) s/2 (or Riesz potential D s  = (−…”
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Extrapolation of Weighted norm inequalities for multivariable operators and applications by Grafakos, Loukas, Martell, José María

“…Two versions of Rubio de Francia’s extrapolation theorem for multivariable operators of functions are obtained. One version assumes an initial estimate with…”
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Maximal Operator and Weighted Norm Inequalities for Multilinear Singular Integrals by Grafakos, Loukas, Torres, Rodolfo H.

“…The maximal operator associated with multilinear Calderón-Zygmund singular integrals is introduced and shown to be bounded on product of Lebesgue spaces…”
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Norm estimates for the fractional derivative of multiple factors by Douglas, Sean, Grafakos, Loukas

“…We extend the Kato-Ponce inequality to a product of m functions, proving an estimate currently missing from the literature. This study is motivated by the fact…”
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Weighted Kato–Ponce inequalities for multiple factors by Douglas, Sean, Grafakos, Loukas

“…In this paper, we establish a weighted Kato–Ponce inequality for m$m$ factors in the endpoint case. Furthermore, we extend the validity of the Kato–Ponce…”
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Corrigendum to “Sharp Hardy Space Estimates for Multipliers” (Int. Math. Res. Not. 2022 (2022): 10403–30) by Grafakos, Loukas, Park, Bae Jun

“…We correct an error in Lemma 4.1 [pages 10420–2] in our article listed in the title. This concerns the cases $s=n$ and $\gamma \leqslant 2$ below, but it does…”
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