Page 487 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 487
HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS (MS-28)
[3] A. Carbonaro, O. Dragicˇevic´, Convexity of power functions and bilinear embedding
for divergence-form operators with complex coefficients, J. Eur. Math. Soc. (JEMS) 22
(2020), no. 10, 3175–3221.
[4] A. Carbonaro, O. Dragicˇevic´, Bilinear embedding for divergence-form operators with
complex coefficients on irregular domains, Calc. Var. Partial Differential Equations 59
(2020), no. 3, Paper No. 104, 36 pp.
[5] A. Carbonaro, O. Dragicˇevic´, V. Kovacˇ, K. Škreb, arXiv 2101.11694 (2021).
[6] A. Cialdea, V. Maz’ya, Criterion for the Lp-dissipativity of second order differential oper-
ators with complex coefficients, J. Math. Pures Appl. 84 (2005), 1067–1100.
[7] M. Dindoš, J. Pipher, Regularity theory for solutions to second order elliptic operators
with complex coefficients and the Lp Dirichlet problem, Adv. Math. 341 255–298 (2019).
[8] M. Egert, On p-elliptic divergence form operators and holomorphic semigroups, On p-
elliptic divergence form operators and holomorphic semigroups, J. Evol. Equ. 20 (2020),
no. 3, 705–724.
Weak L1 inequalities for noncommutative singular integrals
Jose Manuel Conde Alonso, jose.conde@icmat.es
Universidad Autónoma de Madrid, Spain
The classical Calderón-Zygmund decomposition is a fundamental tool that helps one study
endpoint estimates near L1. In this talk, we shall study an extension of the decomposition to a
particular operator valued setting where noncommutativity makes its appearance, allowing us
to get rid of the (usually necessary) UMD property of the Banach space where functions take
values. The noncommutative extension entails a number of applications. One that we shall
discuss concerns weak L1 estimates for Fourier multipliers on groups. Based on joint work
with L. Cadilhac and J. Parcet.
Sobolev-Lorentz capacity and its regularity in the Euclidean setting
Serban Costea, secostea@hotmail.com
University of Pitesti, Romania
We study the Sobolev-Lorentz capacity and its regularity in the Euclidean setting whenever
n ≥ 1 is an integer. We extend here our previous results on the Sobolev-Lorentz capacity
obtained for n > 1 integer. Moreover, for n > 1 integer we obtain a few new results con-
cerning the n, 1 relative and global capacities. Specifically, we obtain sharp estimates for the
n, 1 relative capacity of the concentric condensers (B(0, r), B(0, 1)) for all r in [0, 1). As a
consequence we obtain the exact value of the n, 1 capacity of a point relative to all its bounded
open neighborhoods from Rn when n > 1 is an integer. We also show that this aforementioned
constant is the value of the n, 1 global capacity of any point from Rn, where n > 1 is an integer.
Finally, we prove that whenever n > 1 is an integer, the relative and the global p, 1 capacities
are Choquet whenever p is finite and greater than n.
485
[3] A. Carbonaro, O. Dragicˇevic´, Convexity of power functions and bilinear embedding
for divergence-form operators with complex coefficients, J. Eur. Math. Soc. (JEMS) 22
(2020), no. 10, 3175–3221.
[4] A. Carbonaro, O. Dragicˇevic´, Bilinear embedding for divergence-form operators with
complex coefficients on irregular domains, Calc. Var. Partial Differential Equations 59
(2020), no. 3, Paper No. 104, 36 pp.
[5] A. Carbonaro, O. Dragicˇevic´, V. Kovacˇ, K. Škreb, arXiv 2101.11694 (2021).
[6] A. Cialdea, V. Maz’ya, Criterion for the Lp-dissipativity of second order differential oper-
ators with complex coefficients, J. Math. Pures Appl. 84 (2005), 1067–1100.
[7] M. Dindoš, J. Pipher, Regularity theory for solutions to second order elliptic operators
with complex coefficients and the Lp Dirichlet problem, Adv. Math. 341 255–298 (2019).
[8] M. Egert, On p-elliptic divergence form operators and holomorphic semigroups, On p-
elliptic divergence form operators and holomorphic semigroups, J. Evol. Equ. 20 (2020),
no. 3, 705–724.
Weak L1 inequalities for noncommutative singular integrals
Jose Manuel Conde Alonso, jose.conde@icmat.es
Universidad Autónoma de Madrid, Spain
The classical Calderón-Zygmund decomposition is a fundamental tool that helps one study
endpoint estimates near L1. In this talk, we shall study an extension of the decomposition to a
particular operator valued setting where noncommutativity makes its appearance, allowing us
to get rid of the (usually necessary) UMD property of the Banach space where functions take
values. The noncommutative extension entails a number of applications. One that we shall
discuss concerns weak L1 estimates for Fourier multipliers on groups. Based on joint work
with L. Cadilhac and J. Parcet.
Sobolev-Lorentz capacity and its regularity in the Euclidean setting
Serban Costea, secostea@hotmail.com
University of Pitesti, Romania
We study the Sobolev-Lorentz capacity and its regularity in the Euclidean setting whenever
n ≥ 1 is an integer. We extend here our previous results on the Sobolev-Lorentz capacity
obtained for n > 1 integer. Moreover, for n > 1 integer we obtain a few new results con-
cerning the n, 1 relative and global capacities. Specifically, we obtain sharp estimates for the
n, 1 relative capacity of the concentric condensers (B(0, r), B(0, 1)) for all r in [0, 1). As a
consequence we obtain the exact value of the n, 1 capacity of a point relative to all its bounded
open neighborhoods from Rn when n > 1 is an integer. We also show that this aforementioned
constant is the value of the n, 1 global capacity of any point from Rn, where n > 1 is an integer.
Finally, we prove that whenever n > 1 is an integer, the relative and the global p, 1 capacities
are Choquet whenever p is finite and greater than n.
485
