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...ical analysis]], most spaces which arise in practice turn out to be Banach spaces as well. == Classical Banach spaces == ...

...space]]s of holomorphic functions on the disk. These spaces include the [[Hardy space]]s, the [[Bergman space]]s and [[Dirichlet space]]. ...r norm]] less than 1 on the Hardy spaces <math> H^p(D)</math>, the Bergman spaces <math>A^p(D)</math>. ...

...nvex set]]s are [[domain of holomorphy|domains of holomorphy]]. The Hardy spaces on tubes over convex [[Monge cone|cones]] have an especially rich structure ==Hardy spaces== ...

...]] and [[control theory]], '''''H'''''², or ''H-square'' is a [[Hardy space]] with square norm. It is a subspace of [[Lp space|''L''² ...[orthogonal decomposition]] of <math>L^2(\mathbb{R})</math> into two Hardy spaces ...

| known_for = [[Hardy space]] theory and [[Vanishing mean oscillation|VMO]] ..., 2017) was an American [[mathematician]] whose research topics included [[Hardy space]] theory and [[Vanishing mean oscillation|VMO]]. As a professor at th ...

...elet and Strömberg's motivation was to find an orthonormal basis for the [[Hardy space]]s.<ref name=Stromberg/> ...

...not possible to contain an arbitrary [[Ball (mathematics)#In normed vector spaces|ball]] inside some ''Q'' in Δ (consider, for example, the unit ball centere ...from those. For example, recall the [[Hardy-Littlewood maximal inequality|Hardy-Littlewood Maximal function]] ...

...with the closed curve, such as the [[Szegő kernel|Szegő projection]] onto Hardy space and the [[Neumann–Poincaré operator]], can be expressed in terms of t [[Hardy space]] H²('''T''') consists of the functions for which the nega ...

The [[Hardy–Littlewood inequality]] holds, that is, * The Hardy-Littlewood inequality holds, that is, <math>\int_E|fg|\;d\mu\leq\int_0^\inf ...

...last1=Buliga | first1=Marius|title=Infinitesimal affine geometry of metric spaces endowed with a dilatation structure |year=2010|journal=Houston Journal of M ...calculus goes a long way: [[Sobolev space]]s, differentiation theorems, [[Hardy space]]s. It is noticeable that in such a general situation we don't have e ...

...d completing her Ph.D. in 1993.{{r|cv}} Her doctoral dissertation, ''Hardy Spaces on Strongly Pseudoconvex Domains in <math>C^n</math> and Domains of Finite ...

...y]] of [[measure (mathematics)|measures]] (Pettis) with values in abstract spaces. ...002-9947-1938-1501971-X/S0002-9947-1938-1501971-X.pdf Uniformity in linear spaces], ''Trans. Amer. Math. Soc.'' '''44''' (1938), 305–356.</ref> (with a rema ...

...ry writing deals with function theory and functional analysis, including [[Hardy space]]s, [[De Branges's theorem#Schlicht functions|schlicht function]]s, [ ...y 2004<ref>{{cite journal|author=Rochberg, Richard|title=Review: ''Bergman spaces'', by Peter Duren and Alex Schuster|journal=Bull. Amer. Math. Soc. (N.S.)|y ...

...of a weighted sum of [[radial basis function]]s.<ref>{{cite journal |last1=Hardy |first1=Rolland |title=Multiquadric equations of topography and other irreg ...he basis functions to depend on the interpolation points. In 1971, Rolland Hardy developed a method of interpolating scattered data using interpolants of th ...

...that have a noninteger number of [[derivative]]s are interpolated from the spaces of functions with integer number of derivatives. The theory of interpolation of vector spaces began by an observation of [[Józef Marcinkiewicz]], later generalized and n ...

...class'' for <math>\Omega</math>. The Nevanlinna class includes all the [[Hardy class]]es. ...<math>\exp(-iz)</math> is 1:<ref name=DeBranges>{{cite book|title=Hilbert spaces of entire functions|publisher=Prentice-Hall|author=Louis de Branges|authorl ...

...ant Shah in image processing and made contributions to the theory of Hardy spaces; the contributions were important for [[Analyst's traveling salesman theore | title=Courbes corde-arc et espaces de Hardy généralisés ...

It can be shown that the [[Hardy space]] ''H''^&nbsp;2 is a [[reproducing kernel Hilbert space]], ...ng kernels corresponding to a particular set of reproducing kernel Hilbert spaces, which are related to the set ''R''. It can also be shown that ''f'' is uni ...

...ub>''n''</sub> with ''n'' ≥ 0. Let ''P'' be the orthogonal projection onto Hardy space and set ''T'' = 2''P'' - ''I''. The operator ''H'' = ''iT'' is the '' *{{citation|last=Lehto|first=O.|title=Univalent functions and Teichmüller spaces|year=1987|isbn=0-387-96310-3|publisher=Springer-Verlag|pages=100–101}} ...

...(mathematics)|lemma]] due to [[Frigyes Riesz]], used in the proof of the [[Hardy–Littlewood maximal theorem]]. The lemma was a precursor in one dimension o *{{citation |last=Duren |first=Peter L. |title=Theory of H^p Spaces |publisher=Dover Publications |location=New York |year=2000 |isbn=0-486-411 ...