I am a researcher in analysis, which means I study functions and their properties including smoothness, size, integrability, and approximability, as well as how these properties behave under " reasonably nice" transformations. My specific research interests include harmonic analysis, one and several complex variables, and operator theory. I am particularly interested in projects that combine techniques and ideas from these areas. My PhD thesis focused on weighted estimates for the Bergman and Szego projections. My thesis adviser was Brett Wick: https://www.math.wustl.edu/~wick/. I have also worked on problems related to dyadic operators, Toeplitz and Hankel operators, commutators and BMO, compactness on function spaces, and sampling/dominating sets on Bergman spaces.
Current areas of interest include: Sparse domination, dyadic shift operators and paraproducts, matrix weights, commutators and bounded mean oscillation, Toeplitz and Hankel operators on Bergman spaces, and the Szego projection and Cauchy transform on Lipschitz domains.
Accepted or Published:
Conde-Alonso, Jose M.; Wagner, Nathan A. Endpoint estimates for Haar shift operators with balanced measures. To Appear in Journal of Geometric Analysis. https://arxiv.org/abs/2412.12822
Borges, Tainara; Conde Alonso, Jose M. ; Pipher, Jill; Wagner, Nathan A. Commutator estimates for Haar shifts with general measures. J. Funct. Anal. 289 (2025), no.5, Paper No. 110945. https://arxiv.org/abs/2409.01155
Bell, Steven R.; Lanzani, Loredana; Wagner, Nathan A. A New Way to Express Boundary Values in Terms of Holomorphic Functions on Planar Lipschitz Domains. J. Geom. Anal. 35 (2025), no. 3, Paper No. 98. https://arxiv.org/abs/2409.06611
Conde-Alonso, Jose M.; Pipher, Jill; Wagner, Nathan A. Balanced measures, sparse domination and complexity-dependent weight classes. Balanced measures, sparse domination and complexity-dependent weight classes. Math. Ann. 391 (2025), no. 2, 2209–2253. https://arxiv.org/abs/2309.13943
Green, Walton; Wagner, Nathan A. Weighted Estimates for the Bergman Projection on Planar Domains. Weighted estimates for the Bergman projection on planar domains. Trans. Amer. Math. Soc. 377 (2024), no. 11, 8023–8048.
Hu, Bingyang; Huo, Zhenghui; Lanzani, Loredana; Palencia, Kevin; Wagner, Nathan A. The Commutator of the Bergman Projection on Strongly Pseudoconvex Domains with Minimal Smoothness. J. Funct. Anal. 286 (2024), no. 1, Paper No. 110177, 45 pp. arxiv.org/abs/2210.10640
Stockdale, Cody B. ; Wagner, Nathan A. Weighted theory of Toeplitz operators on the Bergman space. Math. Z. 305 (2023), no. 1, Paper No. 10, 29 pp. https://arxiv.org/abs/2107.03457
Wagner, Nathan A. Some Results for the Szego and Bergman Projections on Planar Domains. Contemp. Math., 792, American Mathematical Society, Providence, RI, 2024, 101–123. https://arxiv.org/abs/2208.14512
Mitkovski, Mishko; Stockdale, Cody B. ; Wagner, Nathan A ; Wick, Brett D. Riesz-Kolmogorov type compactness criteria in function spaces with applications. Complex Anal. Oper. Theory 17 (2023), no. 3, Paper No. 40, 31 pp. https://arxiv.org/abs/2204.14237
Green, A. Walton., Wagner, Nathan. A. Dominating sets in Bergman spaces on strongly pseudoconvex domains. Constr. Approx.59(2024), no.1, 229–269. https://arxiv.org/abs/2107.04400
Stockdale, Cody B.; Wagner, Nathan A. Weighted endpoint bounds for the Bergman and Cauchy-Szegő projections on domains with near minimal smoothness. Indiana Univ. Math. J. 71 (2022), no. 5, 2099–2125. arxiv.org/abs/2005.12261
Balay, Meijke; Neutgens, Trent; Rosen, Nick; Wagner, Nathan; Zeytuncu, Yunus E. Lp regularity of Toeplitz operators on generalized Hartogs triangles. Eur. J. Math. 8 (2022), no. 1, 403–416. arxiv.org/abs/2009.07260
Wagner, Nathan A.; Wick, Brett D. Weighted L^p estimates for the Bergman and Szego projections on strongly pseudoconvex domains with near minimal smoothness. Adv. Math. 384 (2021), Paper No. 107745, 45 pp. arxiv.org/abs/2004.10248
Huo, Zhenghui; Wagner, Nathan A.; Wick, Brett D. Bekollé-Bonami estimates on some pseudoconvex domains. Bull. Sci. Math. 170 (2021), Paper No. 102993, 36 pp. arxiv.org/abs/2001.07868
Adams, Gregory T.; Wagner, Nathan A. A functional decomposition of finite bandwidth reproducing kernel Hilbert spaces. Oper. Matrices 15 (2021), no. 4, 1521–1539. arxiv.org/abs/1908.10822
Huo, Zhenghui; Wagner, Nathan A.; Wick, Brett D. A Békollè-Bonami class of weights for certain pseudoconvex domains. J. Geom. Anal. 31 (2021), no. 6, 6042–6066. arxiv.org/abs/2001.08302
Khodkar, Abdollah; Schulz, Christian; Wagner, Nathan. Existence of Some Signed Magic Arrays. Discrete Mathematics 340 (2017), 906-926. arxiv.org/abs/1701.01649
Gorkin, Pamela; Wagner, Nathan. Ellipses and Compositions of Finite Blaschke Products. Journal of Mathematical Analysis and Analysis 445 (2017), 1354-1366. www.sciencedirect.com/science/article/pii/S0022247X16001013
Preprints:
19. Hu, Bingyang; Li, Ji; Wagner Nathan A. Boundedness and compactness of Bergman projection commutators in two-weight setting. https://arxiv.org/abs/2504.11312
20. de la Cigona, Fernando Benito; Borges, Tainara; D'Emilio, Francesco; Pasquariello, Marcus; Wagner Nathan A. Matrix Weighted L^p Estimates in the Non-Homogeneous Setting. https://arxiv.org/abs/2506.15570
21. Chen, Jiale; Nieraeth, Zoe; Stockdale, Cody B. ; Wagner, Nathan A. Weak-type bounds for the Bergman projection with Bekollé-Bonami weights. https://arxiv.org/abs/2507.22363