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Perälä, Antti
Publications (5 of 5) Show all publications
Perälä, A. & Virtanen, J. (2023). Essential positivity. Proceedings of the American Mathematical Society, 151(11), 4807-4815
Open this publication in new window or tab >>Essential positivity
2023 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 151, no 11, p. 4807-4815Article in journal (Refereed) Published
Abstract [en]

We define essentially positive operators on Hilbert space as a class of self-adjoint operators whose essential spectra is contained in the non-negative real numbers and describe their basic properties. Using Toeplitz operators and the Berezin transform, we further illustrate the notion of essential positivity in the Hardy space and the Bergman space.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2023
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-214456 (URN)10.1090/proc/16504 (DOI)
Available from: 2023-09-15 Created: 2023-09-15 Last updated: 2023-09-15Bibliographically approved
Pang, C., Perälä, A., Wang, M. & Guo, X. (2023). Maximal estimate and integral operators in Bergman spaces with doubling measure. Proceedings of the American Mathematical Society, 151(7), 2881-2894
Open this publication in new window or tab >>Maximal estimate and integral operators in Bergman spaces with doubling measure
2023 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 151, no 7, p. 2881-2894Article in journal (Refereed) Published
Abstract [en]

The boundedness of the maximal operator on the upper half-plane pi+ is established. Here pi+ is equipped with a positive Borel measure d omega(y)dx satisfying the doubling property omega ((0, 2t)) <= C omega ((0, t)). This result is connected to the Carleson embedding theorem, which we use to characterize the boundedness and compactness of the Volterra type integral operators on the Bergman spaces Ap omega(pi+).

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2023
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-214430 (URN)10.1090/proc/14927 (DOI)000973001600001 ()2-s2.0-85174935555 (Scopus ID)
Available from: 2023-09-14 Created: 2023-09-14 Last updated: 2023-11-02Bibliographically approved
Eskandari, S., Abkar, A., Åhag, P. & Perälä, A. (2022). Sub-Hilbert relation for Fock-Sobolev type spaces. New York Journal of Mathematics, 28, 958-969
Open this publication in new window or tab >>Sub-Hilbert relation for Fock-Sobolev type spaces
2022 (English)In: New York Journal of Mathematics, E-ISSN 1076-9803, Vol. 28, p. 958-969Article in journal (Refereed) Published
Abstract [en]

In this paper, two specific sub-Hilbert spaces are studied. They arise from the action of a Toeplitz operator on Fock–Sobolev type spaces, in-duced by a general Gaussian type weight. The argument is based on analysing the reproducing kernel of the corresponding sub-Hilbert space.

Place, publisher, year, edition, pages
Electronic Journals Project, 2022
Keywords
Fock–Sobolev spaces, reproducing kernel, Sub-Fock Hilbert space, Toeplitz operator
National Category
Probability Theory and Statistics Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-198230 (URN)2-s2.0-85133863099 (Scopus ID)
Available from: 2022-07-21 Created: 2022-07-21 Last updated: 2023-12-19Bibliographically approved
Pang, C., Perälä, A. & Wang, M. (2021). Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure. Complex Analysis and Operator Theory, 15(3), Article ID 42.
Open this publication in new window or tab >>Embedding Theorems and Area Operators on Bergman Spaces with Doubling Measure
2021 (English)In: Complex Analysis and Operator Theory, ISSN 1661-8254, E-ISSN 1661-8262, Vol. 15, no 3, article id 42Article in journal (Refereed) Published
Abstract [en]

We establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure dω(y) dx with the doubling property ω(0 , 2 t) ≤ Cω(0 , t). The characterization is given in terms of Carleson squares on the upper half-plane. As special cases, our result covers the standard weights and logarithmic weights. As an application, we also establish the boundedness of the area operator.

Place, publisher, year, edition, pages
Springer nature, 2021
Keywords
Area operator, Carleson measure, Weighted Bergman space
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-181732 (URN)10.1007/s11785-021-01089-4 (DOI)000625116400001 ()2-s2.0-85102043951 (Scopus ID)
Available from: 2021-03-24 Created: 2021-03-24 Last updated: 2023-09-05Bibliographically approved
Liu, C., Perälä, A. & Si, J. (2021). Weighted integrability of polyharmonic functions in the higher-dimensional case. Analysis & PDE, 14(7), 2047-2068
Open this publication in new window or tab >>Weighted integrability of polyharmonic functions in the higher-dimensional case
2021 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 14, no 7, p. 2047-2068Article in journal (Refereed) Published
Abstract [en]

This paper is concerned with the L-p integrability of N-harmonic functions with respect to the standard weights (1 - vertical bar x vertical bar(2))(alpha) on the unit ball B of R-n, n >= 2. More precisely, our goal is to determine the real (negative) parameters alpha for which (1 - vertical bar x vertical bar(2))(alpha/p) u(x) is an element of L-p(B) implies that u equivalent to 0 whenever u is a solution of the N-Laplace equation on B. This question is motivated by the uniqueness considerations of the Dirichlet problem for the N-Laplacian Delta(N).

Our study is inspired by a recent work of Borichev and Hedenmalm (Adv. Math. 264 (2014), 464-505), where a complete answer to the above question in the case n D 2 is given for the full scale 0 < p < infinity. When n >= 3, we obtain an analogous characterization for n-2/n-1 <= p < infinity and remark that the remaining case can be genuinely more difficult. Also, we extend the remarkable cellular decomposition theorem of Borichev and Hedenmalm to all dimensions.

Place, publisher, year, edition, pages
Mathematical Sciences Publishers (MSP), 2021
Keywords
polyharmonic functions, weighted integrability, boundary behavior, cellular decomposition
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:umu:diva-191680 (URN)10.2140/apde.2021.14.2047 (DOI)000733976600002 ()2-s2.0-85114153077 (Scopus ID)
Available from: 2022-01-21 Created: 2022-01-21 Last updated: 2023-03-24Bibliographically approved
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