Embeddings and projections in classical Banach spaces
Embeddings and projections in classical Banach spaces
Paul F. X. Müller
(ORCID: 0000-0002-7081-1365)
Disciplines
Mathematics (100%)
Keywords
-
Geometry of classical Banach spaces,
Anisotropic Haar system,
Mixed-norm spaces,
Embeddings and Projections
We intend to characterize intrinsically large subspaces of classical mixed-norm Banach function spaces. The central object of investigation is the subspace property for mixed norm Hardy spaces. We wish to achieve this by associating canonically a vector measure to the embedding operators of those Banach spaces. Extending these concepts further, we investigate non-commutative Hardy spaces with values in the trace class. Complementing the central themes of our project, we address a long standing conjecture of Maurey. It concerns small subspaces of the Lebesgue space and was formulated for the first time by Maurey in his classical work on fixed point theorems.
The common thread running through our line of research consists in finding intrinsic and useful conditions to decide whether a Banach space is primary. We obtain general conditions in terms of two-player games (strategic reproducibility) as well as specific conditions in classical Banach spaces. These investigations culminate in our very recent capstone result that the Bochner-Lebesgue space L1(Lp) is primary, solving a problem that was well known and remained open for more than 40 years. This line of research was complemented by several results on potential theory and stochastic processes. Specifically, we proved variational estimates for Bloch functions on the unit ball of the n-dimensional Euclidean space, solving a problem open since~1995.
Research institution(s)
- Universität Linz - 100%
International project participants
- Carsten Schütt, Universität Kiel - Germany
- Michal Wojciechowski, IMPAN Warsaw - Poland
- Anna Kamont, Polish Academy of Science - Poland
- David Alonso Gutierrez, Universitat Jaume I - Spain
- Thomas Schlumprecht, Texas A&M University - USA
Research Output
- 200 Citations
- 57 Publications
Publications
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2023
Title Geometrical aspects of lattice gauge equivariant convolutional neural networks DOI 10.48550/arxiv.2303.11448 Type Preprint Author Aronsson J -
2021
Title Generalization capabilities of translationally equivariant neural networks DOI 10.48550/arxiv.2103.14686 Type Preprint Author Bulusu S -
2022
Title Lattice Gauge Equivariant Convolutional Neural Networks DOI 10.1103/physrevlett.128.032003 Type Journal Article Author Favoni M Journal Physical Review Letters Pages 032003 Link Publication -
2022
Title On transverse momentum broadening in real-time lattice simulations of the glasma and in the weak-field limit DOI 10.1051/epjconf/202225805002 Type Journal Article Author Ipp A Journal EPJ Web of Conferences Pages 05002 Link Publication -
2022
Title Equivariance and generalization in neural networks DOI 10.1051/epjconf/202225809001 Type Journal Article Author Bulusu S Journal EPJ Web of Conferences Pages 09001 Link Publication -
2022
Title Preserving gauge invariance in neural networks DOI 10.1051/epjconf/202225809004 Type Journal Article Author Favoni M Journal EPJ Web of Conferences Pages 09004 Link Publication -
2020
Title Strategically reproducible bases and the factorization property DOI 10.1007/s11856-020-2011-2 Type Journal Article Author Lechner R Journal Israel Journal of Mathematics Pages 13-60 Link Publication -
2020
Title Progress on 3+1D Glasma simulations DOI 10.48550/arxiv.2009.02044 Type Preprint Author Ipp A -
2020
Title Almost everywhere convergence of spline sequences DOI 10.1007/s11856-020-2057-1 Type Journal Article Author Müller P Journal Israel Journal of Mathematics Pages 149-177 -
2020
Title Jet momentum broadening in the pre-equilibrium Glasma DOI 10.1016/j.physletb.2020.135810 Type Journal Article Author Ipp A Journal Physics Letters B Pages 135810 Link Publication -
2021
Title The space $L_1(L_p)$ is primary for $1 DOI 10.48550/arxiv.2102.10088 Type Preprint Author Lechner R -
2021
Title On transverse momentum broadening in real-time lattice simulations of the glasma and in the weak-field limit DOI 10.48550/arxiv.2112.03883 Type Preprint Author Ipp A -
2021
Title Hypercontractivity on the unit circle for ultraspherical measures: linear case DOI 10.4171/rmi/1305 Type Journal Article Author Ivanisvili P Journal Revista Matemática Iberoamericana Pages 1335-1348 Link Publication -
2021
Title Generalization capabilities of translationally equivariant neural networks DOI 10.1103/physrevd.104.074504 Type Journal Article Author Bulusu S Journal Physical Review D Pages 074504 Link Publication -
2021
Title Equivariance and generalization in neural networks DOI 10.48550/arxiv.2112.12493 Type Preprint Author Bulusu S -
2021
Title Generalization capabilities of neural networks in lattice applications DOI 10.48550/arxiv.2112.12474 Type Preprint Author Bulusu S -
2021
Title Preserving gauge invariance in neural networks DOI 10.48550/arxiv.2112.11239 Type Preprint Author Favoni M -
2021
Title Lattice gauge symmetry in neural networks DOI 10.48550/arxiv.2111.04389 Type Preprint Author Favoni M -
2021
Title Transverse momentum broadening in real-time lattice simulations of the glasma DOI 10.48550/arxiv.2111.03400 Type Preprint Author Ipp A -
2022
Title Generalization capabilities of neural networks in lattice applications DOI 10.22323/1.396.0400 Type Conference Proceeding Abstract Author Favoni M Pages 400 Link Publication -
2022
Title Lattice Gauge Symmetry in Neural Networks DOI 10.22323/1.396.0185 Type Conference Proceeding Abstract Author Müller D Pages 185 Link Publication -
2022
Title Transverse momentum broadening in real-time lattice simulations of the glasma DOI 10.22323/1.396.0181 Type Conference Proceeding Abstract Author Schuh D Pages 181 Link Publication -
2019
Title Sharp Complex Convexity Estimates DOI 10.48550/arxiv.1901.07926 Type Preprint Author Lindenberger A -
2019
Title Interpolation for Hardy spaces: Marcinkiewicz decomposition, complex interpolation and holomorphic martingales DOI 10.4064/cm7460-10-2018 Type Journal Article Author Müller P Journal Colloquium Mathematicum Pages 141-155 Link Publication -
2019
Title Dimension dependence of factorization problems: Hardy spaces and SLn8 DOI 10.1007/s11856-019-1883-5 Type Journal Article Author Lechner R Journal Israel Journal of Mathematics Pages 677-693 -
2019
Title Dimension dependence of factorization problems: Biparameter Hardy spaces DOI 10.1090/proc/14364 Type Journal Article Author Lechner R Journal Proceedings of the American Mathematical Society Pages 1639-1652 Link Publication -
2019
Title The factorization property of $\ell^\infty(X_k)$ DOI 10.48550/arxiv.1910.11188 Type Preprint Author Lechner R -
2019
Title Subsymmetric weak$^*$ Schauder bases and factorization of the identity DOI 10.4064/sm180404-29-9 Type Journal Article Author Lechner R Journal Studia Mathematica Pages 295-319 Link Publication -
2016
Title Absolutely summing operators and atomic decomposition in bi-parameter Hardy spaces DOI 10.1090/proc/13300 Type Journal Article Author Müller P Journal Proceedings of the American Mathematical Society Pages 1221-1230 Link Publication -
2016
Title Factorization in $SL^\infty$ DOI 10.48550/arxiv.1611.00622 Type Preprint Author Lechner R -
2016
Title Factorization in mixed norm Hardy and BMO spaces DOI 10.48550/arxiv.1610.01506 Type Preprint Author Lechner R -
2016
Title Interpolation for Hardy Spaces: Marcinkiewicz decomposition, Complex Interpolation and Holomorphic Martingales DOI 10.48550/arxiv.1609.07364 Type Preprint Author Müller P -
2016
Title Estimating Averages of Order Statistics of Bivariate Functions DOI 10.1007/s10959-016-0702-8 Type Journal Article Author Lechner R Journal Journal of Theoretical Probability Pages 1445-1470 -
2015
Title Uniform estimates for averages of order statistics of matrices DOI 10.1214/ecp.v20-3992 Type Journal Article Author Lechner R Journal Electronic Communications in Probability Link Publication -
2015
Title LOCALIZATION AND PROJECTIONS ON BI-PARAMETER BMO DOI 10.1093/qmath/hav028 Type Journal Article Author Lechner R Journal The Quarterly Journal of Mathematics Pages 1069-1101 Link Publication -
2018
Title Factorization of the identity through operators with large diagonal DOI 10.1016/j.jfa.2018.02.010 Type Journal Article Author Laustsen N Journal Journal of Functional Analysis Pages 3169-3207 Link Publication -
2018
Title Factorization in mixed norm Hardy and BMO spaces DOI 10.4064/sm8751-6-2017 Type Journal Article Author Lechner R Journal Studia Mathematica Pages 231-265 Link Publication -
2020
Title The factorisation property of l8(Xk) DOI 10.1017/s0305004120000304 Type Journal Article Author Lechner R Journal Mathematical Proceedings of the Cambridge Philosophical Society Pages 421-448 Link Publication -
2020
Title Jet momentum broadening in the pre-equilibrium Glasma DOI 10.48550/arxiv.2009.14206 Type Preprint Author Ipp A -
2020
Title Progress on 3+1D Glasma simulations DOI 10.1140/epja/s10050-020-00241-6 Type Journal Article Author Ipp A Journal The European Physical Journal A Pages 243 Link Publication -
2020
Title Anisotropic momentum broadening in the 2+1D glasma: Analytic weak field approximation and lattice simulations DOI 10.1103/physrevd.102.074001 Type Journal Article Author Ipp A Journal Physical Review D Pages 074001 Link Publication -
2020
Title Radial Variation of Positive Harmonic Functions on Lipschitz Domains DOI 10.48550/arxiv.2003.07176 Type Preprint Author Müller P -
2020
Title Anisotropic momentum broadening in the 2+1D Glasma: analytic weak field approximation and lattice simulations DOI 10.48550/arxiv.2001.10001 Type Preprint Author Ipp A -
2020
Title Lattice gauge equivariant convolutional neural networks DOI 10.48550/arxiv.2012.12901 Type Preprint Author Favoni M -
2020
Title Radial variation of Bloch functions on the unit ball of $\mathbb{R}^d$ DOI 10.4310/arkiv.2020.v58.n1.a10 Type Journal Article Author Müller P Journal Arkiv för Matematik Pages 161-178 Link Publication -
2020
Title Hyper contractivity on the unit circle for ultraspherical measures: linear case DOI 10.48550/arxiv.2004.05567 Type Preprint Author Ivanisvili P -
2015
Title A Decomposition for Hardy Martingales III DOI 10.48550/arxiv.1504.06513 Type Preprint Author Müller P -
2015
Title Factorization of the identity through operators with large diagonal DOI 10.48550/arxiv.1509.03141 Type Preprint Author Laustsen N -
2015
Title Absolutely summing operators and atomic decomposition in bi-parameter Hardy spaces DOI 10.48550/arxiv.1512.04790 Type Preprint Author Müller P -
2018
Title Factorization in SL8 DOI 10.1007/s11856-018-1719-8 Type Journal Article Author Lechner R Journal Israel Journal of Mathematics Pages 957-991 -
2018
Title Strategically reproducible bases and the factorization property DOI 10.48550/arxiv.1809.09423 Type Preprint Author Lechner R -
2018
Title Dimension dependence of factorization problems: Hardy spaces and $SL_n^\infty$ DOI 10.48550/arxiv.1802.02857 Type Preprint Author Lechner R -
2018
Title Subsymmetric weak$^*$ Schauder bases and factorization of the identity DOI 10.48550/arxiv.1804.01372 Type Preprint Author Lechner R -
2018
Title Radial Variation of Bloch functions on the unit ball of $\mathbb{R}^d$ DOI 10.48550/arxiv.1812.01513 Type Preprint Author Müller P -
2018
Title Dimension dependence of factorization problems: bi-parameter Hardy spaces DOI 10.48550/arxiv.1802.05994 Type Preprint Author Lechner R -
2017
Title Almost everywhere Convergence of Spline Sequences DOI 10.48550/arxiv.1711.01859 Type Preprint Author Müller P -
2017
Title Direct sums of finite dimensional $SL^\infty_n$ spaces DOI 10.48550/arxiv.1709.02297 Type Preprint Author Lechner R