Research
My area of interest is Mathematical Analysis, especially Complex Analysis and Operator Theory. My main research is focused on extremal problems in spaces of analytic functions, but I am interested also in other topics within Complex Analysis, Functional Analysis and Operator Theory.
My research has result in the following publications:
Published or accepted works
A. Llinares: Norm of inclusions between some spaces of analytic functions, Banach J. Math. Anal. 16 (2022), no. 1, Paper no. 9, 14 pp.
A. Llinares and D. Vukotić: Contractive inequalities for mixed norm spaces and the Beta function, J. Math. Anal. Appl. 509 (2022), no. 1, Paper no. 125938, 9 pp.
A. Llinares and D. Vukotić: Extremal problems for vanishing functions in Bergman spaces, Proc. Amer. Math. Soc. 150 (2022), no. 6, 2447-2453.
A. Llinares: Contractive inequalities between Dirichlet and Hardy spaces, Rev. Mat. Iberoam. 40 (2024), no. 1, 389-398.
M. Chuaqui, R. Hernández, A. Llinares and A. Mas: On the convolution of convex 2-gons, J. Math. Anal. Appl. 538 (2024), no. 2, Paper no. 128387, 14 pp.
I. Efraimidis, A. Llinares and D. Vukotić: Korenblum's principle for Bergman spaces with radial weights. To appear in Comput. Methods Funct. Theory.
Preprints
A. Llinares: On a conjecture about contractive inequalities for weighted Bergman spaces.
A. Dayan, A. Llinares and K.-M. Perfekt: Restrictions of Békollé-Bonami weights and Bloch functions.
O. F. Brevig, A. Llinares and K. Seip: Critical exponents of the Riesz projection.
The contents of these publications have been shown in the following presentations:
2018: Poster titled On norms of inclusions between mixed norm spaces, presented at conference New Developments in Complex Analysis and Function Theory held in Heraklion (Greece).
2019: Talk titled Norms of inclusions between some classical function spaces, presented at conference Second Madrid International Workshop on Operator Theory and Function Spaces held at Universidad Autónoma de Madrid (Spain).
2019: Poster titled Norms of inclusions between some classical function spaces, presented at conference Biennial Congress of the Spanish Royal Mathematical Society held in Santander (Spain).
2019: Talk titled Norms of inclusions between some classical function spaces, presented at conference Fifth Summer School on Complex Analysis and Operator Theory held in Cullera (Spain).
2019: Talk titled Norms of inclusions between some classical function spaces, presented at conference Second BYMAT Conference: Bring Young Mathematicians Together held at ICMAT (Spain).
2020: Online talk titled Norms of inclusions between some classical function spaces, presented at conference Young Researchers Workshop held in Universidad Complutense de Madrid (Spain).
2021: Online talk titled Contractive inclusions between mixed-norm spaces part of the Complex Analysis and Operator Theory Seminar organized by IMUS (Spain).
2021: Online talk titled Contractive inclusions between mixed-norm spaces part of the Analysis Seminar organized by Department of Mathematical Sciences at NTNU (Norway).
2021: Online talk titled Contractive inclusions between mixed-norm spaces part of the Analysis Seminar organized by Department of Mathematics and Statistics at Texas Tech University (USA).
2021: Online talk titled Contractive inclusions between mixed-norm spaces, presented at conference Focus Program on Analytic Function Spaces and their Applications held at the Fields Institute (Canada).
2022: Talk titled Inclusiones contractivas entre espacios de norma mixta [Contractive inclusions between mixed-norm spaces] part of the Complex Analysis Seminar organized by Departamento de Matemáticas at Universidad Autónoma de Madrid.
2022: Talk titled Normas de inclusión entre espacios de funciones analíticas [Norms of inclusions between spaces of analytic functions] part of the Complex Analysis Workshop organized by Universidad Adolfo Ibáñez at Viña del Mar (Chile).
2022: Talk titled Contractive inequalities between Dirichlet and Hardy spaces part of the Analysis Seminar organized by Department of Mathematical Sciences at NTNU (Norway).
2022: Talk titled Contractive inequalities between Dirichlet and Hardy spaces part of the Analysis Seminar at the University of Belgrade (Serbia).
2022: Talk titled Contractive inequalities between Dirichlet and Hardy spaces, presented at workshop Analysis & Number Theory held at the University of Oslo (Norway).
2023: Talk titled Contractive inequalities for analytic functions part of the Geometric and Functional Analysis Seminar at the University of Helsinki (Finland).
2023: Talk titled Contractive inclusions between spaces of analytic functions part of the Workshop in Mathematical Modeling and Analysis at Umeå University (Sweden).
2023: Talk titled Desigualdades contractivas para espacios de Hilbert de funciones analíticas [Contractive inequalities for Hilbert spaces of analytic functions] part of the Complex Analysis Seminar organized by Departamento de Matemáticas at Universidad Autónoma de Madrid.
2023: Talk titled Contractive inequalities between Dirichlet and Hardy spaces presented at the conference Advanced Courses in Operator Theory and Complex Analysis held at Aristotle University of Thessaloniki (Greece).
2023: Talk titled Contractive inequalities between Dirichlet and Hardy spaces presented at the conference International Workshop on Operator Theory and its Applications held at the University of Helsinki (Finland).
2023: Talk titled On Wolff's theorem for Békollé-Bonami weights part of the Mathematical Modeling and Analysis Seminar organized by Department of Mathematics and Mathematical Statistics at Umeå University.
2023: Talk titled Restricciones de pesos de Békollé-Bonami [Restrictions of Békollé-Bonami weights] part of the Complex Analysis Seminar organized by Departamento de Matemáticas at Universidad Autónoma de Madrid.
2024: Seminar talk at CUNEF Universidad titled What can we do when interpolation is not enough?
2024: Talk titled On Wolff's theorem for Békollé-Bonami weights presented at the conference Spaces of Analytic Functions and their Operators held at the Saarland University (Germany).
Forthcoming talks:
06/06/2024: Seminar talk at Departamento de Matemáticas of the Universidad Carlos III titled On Wolff's theorem for Békollé-Bonami weights.
20/06/2024: Seminar talk at Departamento de Análisis Matemático of the Universidad de Valencia titled On Wolff's theorem for Békollé-Bonami weights.
06/2024: Talk titled What can we do when interpolation is not enough? to be presented at the conference Advances Courses in Operator Theory and its Applications to be held at the Universidad de la Laguna.
I also have given some expository talks, related with my areas of interests.
2016: Talk (jointly with D. Lloria, P. Piniella, J.A. Salmerón and D. Mompeán) titled Análisis armónico de la A a la A [Harmonic Analysis from A to A] presented at conference VI Workshop on Functional Analysis and Applications - XII Encounter of the Spanish Network of Functional Analysis and Applications held in Cáceres (Spain).
2016: Talk (jointly with J.C. Bastons and J. Losada) titled An extremal problem for analytic, bounded and non-vanishing in the disk presented at conference First Workshop on Complex Analysis and Operator Theory held in Málaga (Spain).
2016: Talk titled Series de Dirichlet [Dirichlet series] presented at conference II Congress of Science Students held in Alicante (Spain).
2018: Talk (jointly with A. Mas) titled Desigualdades clásicas con métodos complejos: la desigualdad isoperimétrica [Classical inequalities with complex methods: the isoperimetric inequality] presented at Seminar of the Department of Mathematics at Universidad de Alicante (Spain).
2018: Talk titled Espacios de Hardy y Bergman: una (re)introducción [Hardy and Bergman spaces: a (re)introduction] presented at UAM-ICMAT Junior Seminar at ICMAT (Spain).
2020: Online talk titled La conjetura de Krzyz, o un ejemplo de cómo tirarse de los pelos cuando pierdes la linealidad [The Krzyz Conjecture, or an example of how to pull your hair out when you lose linearity] presented at UAM-ICMAT Junior Seminar.