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Åhag, Per
Publications (10 of 20) Show all publications
Åhag, P. & Czyz, R. (2019). On a characterization of m-subharmonic functions with weak singularities. Annales Polonici Mathematici, 123(1), 21-29
Open this publication in new window or tab >>On a characterization of m-subharmonic functions with weak singularities
2019 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, no 1, p. 21-29Article in journal (Refereed) Published
Abstract [en]

We provide a characterization of functions in Cegrell’s energy class Ep,m.

Keywords
complex Hessian operator, m-subharmonic functions, Cegrell classes
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-165330 (URN)10.4064/ap180628-10-9 (DOI)000493728300004 ()
Available from: 2019-11-27 Created: 2019-11-27 Last updated: 2019-11-27Bibliographically approved
Åhag, P., Cegrell, U. & Hiep, P. H. (2019). On the Guedj-Rashkovskii conjecture. Annales Polonici Mathematici, 123(1), 15-20
Open this publication in new window or tab >>On the Guedj-Rashkovskii conjecture
2019 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, no 1, p. 15-20Article in journal (Refereed) Published
Abstract [en]

We prove some cases when the Guedj-Rashkovskii conjecture holds.

Keywords
complex Monge-Ampere operator, Lelong number, plurisubharmonic function, the Guedj-Rashkovskii conjecture, the residual mass conjecture
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-165332 (URN)10.4064/ap180822-16-11 (DOI)000493728300003 ()
Available from: 2019-11-27 Created: 2019-11-27 Last updated: 2019-11-27Bibliographically approved
Åhag, P. & Czyż, R. (2019). On the Moser-Trudinger inequality in complex space. Journal of Mathematical Analysis and Applications, 479(2), 1456-1474
Open this publication in new window or tab >>On the Moser-Trudinger inequality in complex space
2019 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 479, no 2, p. 1456-1474Article in journal (Refereed) Published
Abstract [en]

In this paper we prove the pluricomplex counterpart of the Moser-Trudinger and Sobolev inequalities in complex space. We consider these inequalities for plurisubharmonic functions with finite pluricomplex energy, and we estimate the concerned constants.

Elsevier, 2019
Keywords
Compact Kahler manifold, Complex Monge-Ampere operator, Plurisubharmonic function, Subharmonic function, Moser-Trudinger inequality, Sobolev inequality
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-162827 (URN)10.1016/j.jmaa.2019.07.006 (DOI)000480510800003 ()
Available from: 2019-09-16 Created: 2019-09-16 Last updated: 2019-09-16Bibliographically approved
Åhag, P., Czyz, R. & Lundow, P.-H. (2018). A counterexample to a conjecture by Blocki-Zwonek. Experimental Mathematics, 27(1), 119-124
Open this publication in new window or tab >>A counterexample to a conjecture by Blocki-Zwonek
2018 (English)In: Experimental Mathematics, ISSN 1058-6458, E-ISSN 1944-950X, Vol. 27, no 1, p. 119-124Article in journal (Refereed) Published
Keywords
Błocki–Zwonek conjectures, Bergman kernel, Green functions, Jacobi functions
National Category
Mathematical Analysis Computational Mathematics
Identifiers
urn:nbn:se:umu:diva-125362 (URN)10.1080/10586458.2016.1230913 (DOI)
Available from: 2016-09-09 Created: 2016-09-09 Last updated: 2018-06-07Bibliographically approved
Åhag, P., Czyż, R. & Hed, L. (2018). Extension and approximation of m-subharmonic functions. Complex Variables and Elliptic Equations, 63(6), 783-801
Open this publication in new window or tab >>Extension and approximation of m-subharmonic functions
2018 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 63, no 6, p. 783-801Article in journal (Refereed) Published
Abstract [en]

Let  be a bounded domain, and let f be a real-valued function defined on the whole topological boundary . The aim of this paper is to find a characterization of the functions f which can be extended to the inside to a m-subharmonic function under suitable assumptions on . We shall do so using a function algebraic approach with focus on m-subharmonic functions defined on compact sets. We end this note with some remarks on approximation of m-subharmonic functions.

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Exhaustion function, m-subharmonic function, Jensen measure, approximation, Dirichlet problem
Mathematics
Identifiers
urn:nbn:se:umu:diva-146810 (URN)10.1080/17476933.2017.1345888 (DOI)000428782900003 ()
Available from: 2018-04-26 Created: 2018-04-26 Last updated: 2018-06-09Bibliographically approved
Åhag, P., Czyz, R. & Hed, L. (2018). The Geometry of m-Hyperconvex Domains. Journal of Geometric Analysis, 28(4), 3196-3222
Open this publication in new window or tab >>The Geometry of m-Hyperconvex Domains
2018 (English)In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 28, no 4, p. 3196-3222Article in journal (Refereed) Published
Abstract [en]

We study the geometry of m-regular domains within the Caffarelli–Nirenberg–Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We prove among other things that every m-hyperconvex domain admits an exhaustion function that is negative, smooth, strictly m-subharmonic, and has bounded m-Hessian measure.

Springer, 2018
Keywords
Barrier function, Caffarelli-Nirenberg-Spruck model, Exhaustion function, m-subharmonic function, Jensen measure
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-154928 (URN)10.1007/s12220-017-9957-2 (DOI)000451728700010 ()30595641 (PubMedID)
Available from: 2019-01-07 Created: 2019-01-07 Last updated: 2019-01-07Bibliographically approved
Åhag, P., Cegrell, U. & Phạm, H. H. (2015). Monge-Ampère measures on subvarieties. Journal of Mathematical Analysis and Applications, 423, 94-105
Open this publication in new window or tab >>Monge-Ampère measures on subvarieties
2015 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 423, p. 94-105Article in journal (Refereed) Published
Abstract [en]

In this article we address the question whether the complex Monge-Ampere equation is solvable for measures with large singular part. We prove that under some conditions there is no solution when the right-hand side is carried by a smooth subvariety in C-n of dimension k < n.

Keywords
Complex Monge-Ampere operator,  Dirichlet problem,  Pluripolar set,  Plurisubharmonic function
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-93533 (URN)10.1016/j.jmaa.2014.09.061 (DOI)000349706000008 ()
Available from: 2014-09-23 Created: 2014-09-23 Last updated: 2018-06-07Bibliographically approved
Åhag, P. & Czyz, R. (2015). On the Blocki-Zwonek conjectures. Complex Variables and Elliptic Equations, 60(9), 1270-1276
Open this publication in new window or tab >>On the Blocki-Zwonek conjectures
2015 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 60, no 9, p. 1270-1276Article in journal (Refereed) Published
Abstract [en]

Let Omega be a bounded pseudoconvex domain in C-n, and let g(Omega) (z, a) be the pluricomplex Green function with pole at a in Omega. It was conjectured by Blocki and Zwonek that the function given by beta = beta(Omega),(a) : (-infinity, 0) (sic) t -> beta(t) = log (lambda(n)({z is an element of Omega g(Omega) (z, a) < t})) is convex. Here.n is the Lebesgue measure in Cn. In this note we give an affirmative answer to this conjecture when Omega is biholomorphic to the unit ball or to the polydisc in C-n, n >= 1.

Keywords
Bergman kernel, Bocki-Zwonek conjectures, pluricomplex Green functions
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-97712 (URN)10.1080/17476933.2015.1004541 (DOI)000359478400007 ()
Available from: 2015-01-07 Created: 2015-01-07 Last updated: 2018-06-07Bibliographically approved
Åhag, P. & Czyż, R. (2015). On the Blocki-Zwonek conjectures and beyond. Archiv der Mathematik, 105(4), 371-380
Open this publication in new window or tab >>On the Blocki-Zwonek conjectures and beyond
2015 (English)In: Archiv der Mathematik, ISSN 0003-889X, E-ISSN 1420-8938, Vol. 105, no 4, p. 371-380Article in journal (Refereed) Published
Abstract [en]

Let $${\Omega}$$ be a bounded pseudoconvex domain in $${\mathbb{C}^n}$$, and let $${g_{\Omega}(z,a)}$$ be the pluricomplex Green function with pole at a in $${\Omega}$$. Błocki and Zwonek conjectured that the function given by $$\begin{array}{ll}\alpha = \alpha_{\Omega}, a: (- \infty, 0) \ni t \mapsto \alpha (t) = e^{-2nt} \lambda_n \left( \{z \in \Omega: g_{\Omega}(z, a) < t \} \right)\end{array}$$ is nondecreasing, and that the function given by $$\begin{array}{ll}\beta = \beta_{\Omega}, a: (-\infty, 0) \ni t \to \beta(t)= \log \left(\lambda_n \left(\{z \in \Omega: g_{\Omega}(z,a)< t\}\right)\right)\end{array}$$ is convex. Here $${\lambda_{n}}$$ is the Lebesgue measure in $${\mathbb{C}^n}$$. In this note we give an affirmative answer to these conjectures when $${\Omega}$$ is biholomorphic to a bounded, balanced, and pseudoconvex domain in $${\mathbb{C}^n}$$, $${n\geq 1}$$. The aim of this note is to consider generalizations of the functions $${\alpha}$$, $${\beta}$$ defined by the Green function with two poles in $${\mathbb{D}\subset\mathbb{C}}$$. We prove that $${\alpha}$$ is not nondecreasing, and $${\beta}$$ is not convex. By using the product property for pluricomplex Green functions, we then generalize this to n-dimensions. Finally, we end this note by considering two other possibilities generalizing the Błocki–Zwonek conjectures.

Springer, 2015
Keywords
Bergman kernel, Błocki–Zwonek conjectures, Pluricomplex Green functions
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-106678 (URN)10.1007/s00013-015-0810-1 (DOI)000361347100009 ()
Available from: 2015-08-01 Created: 2015-08-01 Last updated: 2018-06-07Bibliographically approved
Åhag, P., Cegrell, U. & Czyz, R. (2015). Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge-Ampere operator. Journal of Mathematical Analysis and Applications, 422(2), 960-980
Open this publication in new window or tab >>Vector spaces of delta-plurisubharmonic functions and extensions of the complex Monge-Ampere operator
2015 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 422, no 2, p. 960-980Article in journal (Refereed) Published
Abstract [en]

In this paper we shall consider two types of vector ordering on the vector space of differences of negative plurisubharmonic functions, and the problem whether it is possible to construct supremum and infimum. Then we consider two different approaches to define the complex Monge-Ampere operator on these vector spaces, and we solve some Dirichlet problems. We end this paper by stating and discussing some open problems.

Keywords
Complex Monge-Ampere operator, Delta-plurisubharmonic function, Pluricomplex energy, urisubharmonic function, Vector ordering
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-98542 (URN)10.1016/j.jmaa.2014.09.022 (DOI)000344911800012 ()
Available from: 2015-01-30 Created: 2015-01-23 Last updated: 2018-06-07Bibliographically approved

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