Abstract
Let W be a finite reflection group associated with a root system R in
Funding statement: P. Plewa acknowledges the financial support of Compagnia di San Paolo.
References
[1]
P. Auscher and E. Russ,
Hardy spaces and divergence operators on strongly Lipschitz domains of
[2]
P. Auscher and E. Russ,
Hardy spaces and divergence operators on strongly Lipschitz domains of
[3]
P. Auscher, E. Russ and P. Tchamitchian,
Hardy Sobolev spaces on strongly Lipschitz domains of
[4]
D.-C. Chang,
The dual of Hardy spaces on a bounded domain in
[5]
D.-C. Chang, G. Dafni and E. M. Stein,
Hardy spaces, BMO, and boundary value problems for the Laplacian on a smooth domain in
[6]
D.-C. Chang, S. G. Krantz and E. M. Stein,
[7] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645. 10.1090/S0002-9904-1977-14325-5Search in Google Scholar
[8] J. B. Conway, A Course in Functional Analysis, 2nd ed., Grad. Texts in Math. 96, Springer, New York, 1990. Search in Google Scholar
[9] M. Costabel, A. McIntosh and R. J. Taggart, Potential maps, Hardy spaces, and tent spaces on special Lipschitz domains, Publ. Mat. 57 (2013), no. 2, 295–331. 10.5565/PUBLMAT_57213_02Search in Google Scholar
[10] D. Deng, X. T. Duong, A. Sikora and L. Yan, Comparison of the classical BMO with the BMO spaces associated with operators and applications, Rev. Mat. Iberoam. 24 (2008), no. 1, 267–296. 10.4171/RMI/536Search in Google Scholar
[11] C. F. Dunkl and Y. Xu, Orthogonal Polynomials of Several Variables, Encyclopedia Math. Appl. 81, Cambridge University, Cambridge, 2001. 10.1017/CBO9780511565717Search in Google Scholar
[12] X. T. Duong and L. Yan, Duality of Hardy and BMO spaces associated with operators with heat kernel bounds, J. Amer. Math. Soc. 18 (2005), no. 4, 943–973. 10.1090/S0894-0347-05-00496-0Search in Google Scholar
[13] J. García-Cuerva and J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud. 116, North-Holland, Amsterdam, 1985. Search in Google Scholar
[14] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Stud. Adv. Math. 29, Cambridge University, Cambridge, 1990. 10.1017/CBO9780511623646Search in Google Scholar
[15]
A. Jonsson, P. Sjögren and H. Wallin,
Hardy and Lipschitz spaces on subsets of
[16] R. Kane, Reflection Groups and Invariant Theory, CMS Books Math./Ouvrages Math. SMC 5, Springer, New York, 2001. 10.1007/978-1-4757-3542-0Search in Google Scholar
[17]
J. Małecki and K. Stempak,
Reflection principles for functions of Neumann and Dirichlet Laplacians on open reflection invariant subsets of
[18]
A. Miyachi,
[19] S. Semmes, A primer on Hardy spaces, and some remarks on a theorem of Evans and Müller, Comm. Partial Differential Equations 19 (1994), no. 1–2, 277–319. 10.1080/03605309408821017Search in Google Scholar
[20] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University, Princeton, 1970. 10.1515/9781400883882Search in Google Scholar
[21] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Ser. 43, Princeton University, Princeton, 1993. 10.1515/9781400883929Search in Google Scholar
[22] K. Stempak, Finite reflection groups and symmetric extensions of Laplacian, Studia Math. 261 (2021), no. 3, 241–267. 10.4064/sm200423-19-11Search in Google Scholar
[23] K. Stempak, The Laplacian with mixed Dirichlet–Neumann boundary conditions on Weyl chambers, J. Differential Equations 329 (2022), 348–370. 10.1016/j.jde.2022.05.005Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
- Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
- Connections and genuinely ramified maps of curves
- Caustics of pseudo-spherical surfaces in the Euclidean 3-space
- On liftings of modular forms and Weil representations
- Approximation via statistical measurable convergence with respect to power series for double sequences
- Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
- Gem-induced trisections of compact PL 4-manifolds
- Categories of modules, comodules and contramodules over representations
- On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
- On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
- Hardy and BMO spaces on Weyl chambers
- De Branges–Rovnyak spaces and local Dirichlet spaces of higher order
Articles in the same Issue
- Frontmatter
- On Mukhin’s necessary and sufficient condition for the validity of the local limit theorem
- Non-commutative Khinchine-type inequality for dependent random variables and overview of its applications in data science
- Connections and genuinely ramified maps of curves
- Caustics of pseudo-spherical surfaces in the Euclidean 3-space
- On liftings of modular forms and Weil representations
- Approximation via statistical measurable convergence with respect to power series for double sequences
- Global existence, scattering, rigidity and inverse scattering for some quasilinear hyperbolic systems
- Gem-induced trisections of compact PL 4-manifolds
- Categories of modules, comodules and contramodules over representations
- On the Iwasawa invariants of BDP Selmer groups and BDP p-adic L-functions
- On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
- Congruence subgroups and crystallographic quotients of small Coxeter groups
- Some Betti numbers of the moduli of 1-dimensional sheaves on ℙ2
- Hardy and BMO spaces on Weyl chambers
- De Branges–Rovnyak spaces and local Dirichlet spaces of higher order