zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Morrey spaces for non-doubling measures. (English) Zbl 1129.42403
Summary: The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.

42B35Function spaces arising in harmonic analysis
42B25Maximal functions, Littlewood-Paley theory
[1]Gilberg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order, 2nd ed., Springer– Verlag, Berlin, 1983
[2]García–Cuerva, J., Rubio de Francia, J. L.: Weighted Norm Inequalities and Related Topics. North–Holland Math. Stud., 116, (1985)
[3]Stein, E. M.: Harmonic Analysis: Real–Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, 1993
[4]Nazarov, F., Treil, S., Volberg, A.: Weak type estimates and Cotlar inequalities for Calderón–Zygmund operators on nonhomogeneous spaces, Internat. Math. Res. Notices 463–487, 1998
[5]Tolsa, X.: Littlewood–Paley theory and the T(1) theorem with non–doubling measures. Adv. Math., 164, 57–116 (2001) · Zbl 1015.42010 · doi:10.1006/aima.2001.2011
[6]Tolsa, X.: BMO, H 1, and Calderón–Zygmund operators for non doubling measures. Math. Ann., 319, 89–149 (2001) · doi:10.1007/PL00004432
[7]Han, Y., Yang, D.: Triebel–Lizorkin spaces for non doubling measures. Studia Math., 164, 105–140 (2004) · Zbl 1098.42018 · doi:10.4064/sm162-2-2
[8]Deng, D., Han, Y., Yang, D.: Besov spaces with non doubling measures. Trans. Amer. Math. Soc., to appear
[9]Adams, D.: A note on Riesz potentials. Duke Math. J., 42, 765–778 (1975) · Zbl 0336.46038 · doi:10.1215/S0012-7094-75-04265-9
[10]Chiarenza, F., Frasca, M.: Morrey spaces and Hardy–Littlewood maximal function. Rend. Mat., 7, 273–279 (1987)
[11]Komori, Y.: Calderón–Zygmund operators on the predual of a Morrey space. Acta Mathematica Sinica, English Series, 19(2), 297–302 (2003) · Zbl 1031.42011 · doi:10.1007/s10114-002-0226-2
[12]Sawano, Y.: Sharp estimates of the modified Hardy–Littlewood maximal operator on the nonhomogeneous space via covering lemmas. Hokkaido Math. J., 34, 435–458 (2005)
[13]García–Cuerva, J., Gatto, E.: Boundedness properties of fractional integral operators associated to nondoubling measures. Studia Math., 162(3), 245–261 (2004) · Zbl 1045.42006 · doi:10.4064/sm162-3-5
[14]Chen, W., Sawyer, E.: A note on commutators of fractional integrals with RBMO(μ) functions. Illinois J. Math., 46(4), 1287–1298 (2002)
[15]García–Cuerva, J., Martell, J. M.: Weighted inequalities and vector–valued Calderón–Zygmund operators on nonhomogeneous spaces. Publ. Mat., 44(2), 613–640 (2000)