LEADER 03035nam a2200337 i 4500 001 991002944279707536 008 160712s2015 sz a ob 001 0 eng d 020 $a9783319181318 035 $ab14258092-39ule_inst 040 $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng 082 04$a515.7$223 084 $aAMS 42B35 084 $aAMS 30L05 084 $aAMS 35J57 100 1 $aAlvarado, Ryan$0716353 245 10$aHardy spaces on Ahlfors-regular quasi metric spaces :$ba sharp theory /$cRyan Alvarado, Marius Mitrea 260 $aCham [Switzerland] :$bSpringer,$cc2015 300 $aviii, 486 p. :$bill. ;$c24 cm 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2142 504 $aIncludes bibliographical references and indexes 505 0 $aIntroduction - Geometry of Quasi-Metric Spaces -- Analysis on Spaces of Homogeneous Type -- Maximal Theory of Hardy Spaces -- Atomic Theory of Hardy Spaces -- Molecular and Ionic Theory of Hardy Spaces -- Further Results -- Boundedness of Linear Operators Defined on Hp(X) -- Besov and Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces 520 $aSystematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Ahlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part gives atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-contained and is intended for an audience of mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry 650 0$aHardy spaces 650 0$aQuasi-metric spaces 700 1 $aMitrea, Marius$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0441111 907 $a.b14258092$b22-11-16$c12-07-16 912 $a991002944279707536 945 $aLE013 42B ALV11 (2015)$g1$i2013000293790$lle013$op$pE72.79$q-$rl$s- $t0$u1$v0$w1$x0$y.i15788982$z22-11-16 996 $aHardy spaces on Ahlfors-regular quasi metric spaces$91413242 997 $aUNISALENTO 998 $ale013$b12-07-16$cm$da $e-$feng$gsz $h0$i0