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New Progress on Weighted Trudinger–Moser and Gagliardo–Nirenberg, and Critical Hardy Inequalities on Stratified Groups

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Landscapes of Time-Frequency Analysis

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

In this paper, we present a summary of our recent research on local and global weighted (singular) Trudinger–Moser inequalities with remainder terms, critical Hardy-type and weighted Gagliardo–Nirenberg inequalities on general stratified groups. These include the cases of \(\mathbb R^n\) and Heisenberg groups. Moreover, the described critical Hardy-type inequalities give the critical case of the Hardy-type inequalities from [4].

The first author was supported by the EPSRC Grant EP/R003025/1, by the Leverhulme Research Grant RPG-2017-151, and by the FWO Odysseus grant. The second author was supported by the MESRK grant AP05133271. No new data was collected or generated during the course of research.

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Author information

Authors and Affiliations

  1. Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium and School of Mathematical Sciences, Queen Mary University of London, London, UK

    Michael Ruzhansky

  2. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, UK

    Nurgissa Yessirkegenov

  3. Institute of Mathematics and Mathematical Modelling, 125 Pushkin Street, 050010, Almaty, Kazakhstan

    Nurgissa Yessirkegenov

Authors
  1. Michael Ruzhansky
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  2. Nurgissa Yessirkegenov
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Correspondence to Michael Ruzhansky .

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica “G. Peano”, University of Torino, Turin, Italy

    Paolo Boggiatto

  2. Dipartimento di Matematica “G. Peano”, University of Torino, Turin, Italy

    Elena Cordero

  3. Faculty of Mathematics, University of Vienna, Vienna, Austria

    Maurice de Gosson

  4. Faculty of Mathematics, University of Vienna, Vienna, Austria

    Hans G. Feichtinger

  5. Department of Mathematical Sciences, Polytechnic University of Torino, Turin, Italy

    Fabio Nicola

  6. Dipartimento di Matematica “G. Peano”, University of Torino, Turin, Italy

    Alessandro Oliaro

  7. Department of Mathematical Sciences, Polytechnic University of Torino, Turin, Italy

    Anita Tabacco

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Ruzhansky, M., Yessirkegenov, N. (2019). New Progress on Weighted Trudinger–Moser and Gagliardo–Nirenberg, and Critical Hardy Inequalities on Stratified Groups. In: Boggiatto, P., et al. Landscapes of Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05210-2_11

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