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Mathematics

D-Index
42
Citations
11444
World Ranking
1753
National Ranking
749

Overview

Loukas Grafakos is affiliated with the University of Missouri in the United States. Their research primarily focuses on the field of Mathematics, with a total of 124 publications. Within this broad area, they specialize in subfields including Applied Mathematics, Mathematical Physics, Numerical Analysis, Statistics and Probability, and Computer Vision and Pattern Recognition.

The main topics covered in their work reflect a strong emphasis on harmonic analysis and advanced mathematical theory. These topics include:

  • Advanced Harmonic Analysis Research
  • Mathematical Analysis and Transform Methods
  • Advanced Mathematical Physics Problems
  • Nonlinear Partial Differential Equations
  • Advanced Banach Space Theory
  • Approximation Theory and Sequence Spaces
  • Mathematical Approximation and Integration

Grafakos has authored numerous papers, with recent works including:

  • "Fractional Fourier transforms on L and applications" (2021), published in Applied and Computational Harmonic Analysis
  • "Riesz transform associated with the fractional Fourier transform and applications in image edge detection" (2023), published in Applied and Computational Harmonic Analysis
  • "The Bourgain-Brezis-Mironescu formula on ball Banach function spaces" (2023), published in Mathematische Annalen
  • "Some Remarks on the Mikhlin-Hörmander and Marcinkiewicz Multiplier Theorems: A Short Historical Account and a Recent Improvement" (2021), published in Journal of Geometric Analysis
  • "Multiplier conditions for Boundedness into Hardy spaces" (2021), published in Annales de l'institut Fourier

The venues where Grafakos often publishes reflect a range of mathematical journals and platforms, including:

  • arXiv (Cornell University)
  • Studia Mathematica
  • Applied and Computational Harmonic Analysis
  • International Mathematics Research Notices
  • Transactions of the American Mathematical Society

The scientist has frequently collaborated with several other researchers, among them:

  • Bae Jun Park
  • Petr Honzík
  • Danqing He
  • Zunwei Fu
  • Yue Wu

Grafakos has also contributed to academic literature through book publications. A notable example is the book Fundamentals of Fourier Analysis, published by Springer Nature in 2024.

Best Publications

  • Classical Fourier Analysis

    Loukas Grafakos

  • Classical and modern Fourier analysis

    Loukas Grafakos

  • Modern Fourier analysis

    Loukas Grafakos

  • Multilinear Calderón–Zygmund Theory

    Loukas Grafakos;Rodolfo H. Torres

  • The Kato-Ponce Inequality

    Loukas Grafakos;Seungly Oh

  • Maximal operator and weighted norm inequalities for multilinear singular integrals

    Loukas Grafakos;Rodolfo H. Torres

  • Best constants for two nonconvolution inequalities

    Michael Christ;Loukas Grafakos

  • Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces

    Oliver Dragicevic;Loukas Grafakos;María Cristina Pereyra;Stefanie Petermichl

  • Some remarks on multilinear maps and interpolation

    Loukas Grafakos;Nigel Kalton

  • L p BOUNDS FOR SINGULAR INTEGRALS AND MAXIMAL SINGULAR INTEGRALS WITH ROUGH KERNELS

    Loukas Grafakos;Atanas Stefanov

  • On multilinear fractional integrals

    Loukas Grafakos

  • Vector-valued singular integrals and maximal functions on spaces of homogeneous type

    Loukas Grafakos;Liguang Liu;Dachun Yang

  • On multilinear singular integrals of Calderón-Zygmund type

    Loukas Grafakos;Rodolfo H. Torres

  • Extrapolation of Weighted norm inequalities for multivariable operators and applications

    Loukas Grafakos;Loukas Grafakos;José María Martell;José María Martell

  • Multilinear Calderón-Zygmund operators on Hardy spaces

    Loukas Grafakos;Nigel J. Kalton

  • Uniform bounds for the bilinear Hilbert transforms, I

    Loukas Grafakos;Xiaochun Li

  • On Multilinear Fourier Multipliers of Limited Smoothness

    Loukas Grafakos;Akihiko Miyachi;Naohito Tomita

  • The Marcinkiewicz multiplier condition for bilinear operators

    Loukas Grafakos;Nigel J. Kalton

  • Maximal function characterizations of Hardy spaces on RD-spaces and their applications

    Loukas Grafakos;LiGuang Liu;DaChun Yang

  • On Fourier Transforms of Radial Functions and Distributions

    Loukas Grafakos;Gerald Teschl;Gerald Teschl

  • Multilinear Calder'on-Zygmund operators on Hardy spaces

    Loukas Grafakos;Nigel Kalton

  • Spaces of Lipschitz and Hölder functions and their applications

    Fritz Gesztesy;Gilles Godefroy;Loukas Grafakos;Igor Verbitsky

Frequent Co-Authors

Gilles Godefroy
Gilles Godefroy Institut de Mathématiques de Jussieu
Fritz Gesztesy
Fritz Gesztesy Baylor University
Nigel J. Kalton
Nigel J. Kalton University of Missouri
Rodolfo H. Torres
Rodolfo H. Torres University of California, Riverside
Dachun Yang
Dachun Yang Beijing Normal University
Andreas Seeger
Andreas Seeger University of Wisconsin–Madison
Terence Tao
Terence Tao University of California, Los Angeles
José María Martell
José María Martell Institute of Mathematical Sciences
Michael Christ
Michael Christ University of California, Berkeley
Xiaochun Li
Xiaochun Li University of California, Los Angeles

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