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2-polyhedron algebra arbitrary assume Banach space Bellman function belongs Blaschke product bounded Calderon-Zygmund Carleson coefficient space coincides constant construction converges convex Corollary corresponding curve decomposition deduce defined definition denote Dirichlet domain dyadic element embedding theorem English transl equation equivalent estimate exists factor family of cubes finite fixed follows formula Haar system Hardy spaces Hecke operators Hilbert space Hilbert transformation Holder inequality homogeneous homomorphism implies inequality inner function integral interval isomorphism kernel key property Lemma linear LP(W mapping Math matrix modular forms multiplicity norm obtain pair piecewise smooth piecewise smooth metric Poincare metric polynomial positive problem proof of Theorem Proposition prove quadratic forms recall relation Remark representation respect result right-hand side satisfying scalar sequence signed curvature measure singular solution strong unconditional basis Subsection subspace suffices symmetric Theorem theta-functions theta-series variables vector weight whence zero