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)
Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality. (English) Zbl 0959.47028
Consider the Schrödinger operator $-A=\Delta -V$ in ${\Bbb R}^d$, where $V$ is nonnegative and satisfies the reverse Hölder inequality with exponent $q>d/2$ (i.e., $(|B|^{-1}\int_B V^q dx)^{1/q}\leq C|B|^{-1}\int_b V dx$ for every ball $B$). Let $T_t$ be the semigroup of linear operators generated by $-A$, and let $Mf(x)=\sup_{t>0} |T_t f(x)|$. The Hardy space $H^1_A$ is defined to be $\{ f: Mf\in L^1\}$. It is shown that $H^1_A$ can be described in terms of atomic decomposition, much as in the case of the classical real variable $H^1$, though the notion of an atom is different. The operators $R_J=(\partial/\partial x_j)A^{-1/2}$ are analogs of the Riesz transforms. It is shown that $H^1_A=\{ f\in L^1:R_j f\in L^1, 1\leq j\leq d \}$.

47F05Partial differential operators
46J15Banach algebras of differentiable or analytic functions, $H^p$-spaces
42B30$H^p$-spaces (Fourier analysis)
43A80Analysis on other specific Lie groups
47D06One-parameter semigroups and linear evolution equations
Full Text: DOI EuDML