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)
Function spaces on local fields. (English) Zbl 1113.46069
Summary: We study function spaces on local fields, such as Triebel B-type and F-type spaces, Hölder type spaces, Sobolev type spaces, etc. Moreover, we study the relationship between the p-type derivatives and the Hölder type spaces. Our results show that there exists quite a difference between the functions defined on Euclidean spaces and local fields, respectively. Furthermore, many properties of functions defined on local fields motivate the new idea of solving some important problems in fractal analysis.
46S10Functional analysis over fields (not , , or quaternions)
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
[1]Su, W. Y., Pseudo-differential operators in Besov spaces over local fields, ATA, 1988, 4(2): 119–129.
[2]Su, W. Y., Pseude-differential operators and derivatives on locally compact Vilenkin groups, Science in China, Ser. A, 1992, 35(7): 826–836.
[3]Su, W. Y., Gibbs-Butzer derivatives and their applications, Numer. Funct. Anal. Optimiz., 1995, 16(5-6): 805–824. · Zbl 0831.42020 · doi:10.1080/01630569508816646
[4]Su, W. Y., Gibbs-Butzer differential operators and on locally compact Vilenkin groups, Science in China, Ser. A, 1996, 39(7): 718–727.
[5]Su, W. Y., Liu G. Q., The boundedness of certain operators on Holder and Sobolev spaces, ATA, 1997, 13(1): 18–32.
[6]Su, W. Y., Calculus on fractals based upon local fields, ATA, 2000, 16(1): 93–100.
[7]Taibleson, M., Fourier Analysis on Local Fields, Princeton: Princeton Univ. Press, 1975.
[8]Triebel, H., Theory of Function Spaces, Basel: Birkhauser Verlag, 1983.
[9]Triebel, H., Fractals and Spectra, Basel: Birkhauser Verlag, 1997.
[10]Triebel, H., The Structure of Functions, Basel: Birkhauser Verlag, 2001.
[11]Jiang, H. K., The derivatives and integrals of fractional on α-adic groups, Chinese Ann. of Math., 1993, 14B(4): 515–526.
[12]Onneweer, C. W., Differentiation on a p-adic or p-series fields, in Linear Spaces and Approx., Basel: Birkhauser Verlag Basel, 1978, 187–198.
[13]Zheng, W. X., Derivatives and approximation theorems on local fields, Rocky Mountain J. of Math., 1985, 15(4): 803–817.
[14]Zheng, W. X., Su, W. Y., Jiang, H. K., A note to the concept of derivatives on local fields, ATA, 1990, 6(3): 48–58.