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1.
Jie Miao 《Integral Equations and Operator Theory》1997,27(4):426-438
We study Toeplitz operators on the harmonic Bergman spaceb
p
(B), whereB is the open unit ball inR
n(n2), for 1<p. We give characterizations for the Toeplitz operators with positive symbols to be bounded, compact, and in Schatten classes. We also obtain a compactness criteria for the Toeplitz operators with continuous symbols. 相似文献
2.
Compact Hankel operators on harmonic Bergman spaces 总被引:2,自引:0,他引:2
Mirjana Jovović 《Integral Equations and Operator Theory》1995,22(3):295-304
We study Hankel operators on the harmonic Bergman spaceb
2(B), whereB is the open unit ball inR
n,n2. We show that iff is in
then the Hankel operator with symbolf is compact. For the proof we have to extend the definition of Hankel operators to the spacesb
p(B), 1<p<, and use an interpolation theorem. We also use the explicit formula for the orthogonal projection ofL
2(B, dV) ontob
2(B). This result implies that the commutator and semi-commutator of Toeplitz operators with symbols in
are compact. 相似文献
3.
Eun Sun Choi 《Czechoslovak Mathematical Journal》2008,58(1):93-111
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations
of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space b
p
into another b
q
for 1 < p, q < ∞ in terms of certain Carleson and vanishing Carleson measures.
This research was supported by KOSEF (R01-2003-000-10243-0) and Korea University Grant. 相似文献
4.
V. A. Tolokonnikov 《Journal of Mathematical Sciences》1987,37(5):1359-1364
In this paper one considers some general theorems of the theory of Hankel and Toeplitz operators in spaces of analytic functions. Under natural restrictions on the spaces X, it is shown that the symbols of the Toeplitz operators, acting in X, are bounded. One describes completely the symbols of the Hankel and Toeplitz operators, acting from Hp into ¯Hq (into Hq) for 0 < p, q < .Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 141, pp. 165–175, 1985.The author expresses his gratitude to A. L. Vol'berg and S. V. Kislyakov for useful discussions. 相似文献
5.
Pham Loi Vu 《Acta Appl Math》2004,84(1):97-120
The paper deals with a problem of developing an inverse-scattering based formalism for solving problems for the cubic nonlinear (or the modified Korteweg–de Vries (KdV)) equations: q
t
+q
xxx
+6q
2
q
x
=0, 0x<, –<t<,q
t
+q
xxx
–6q
2
q
x
=0, with the given initial and boundary conditions: q(x,0)=q(x),q(0,t)=p(t), p(t)L
1(–,). The relation between the solution of the initial-boundary value problem (1), (3), (4) and that of the KdV equation on the half-line is shown. The Cauchy problem for the cubic nonlinear equation: q
t
+q
xxx
–6|q|2
q
x
=0, 0x<, –<t<, with the given initial condition (3) is considered also. Here we solve the above problems on the half-line 0x< but with –<t<. 相似文献
6.
We establish a Fredholm criterion and an index formula for Toeplitz operators with semi-almost-periodic matrix symbols on the Hardy spaces H
p
(1<p<). Our main result completes the Fredholm theory of the aforementioned operators and generalizes previous results, which concerned the case p=2 or were based on certain additional assumptions, such as factorizability, for the almost-periodic representatives of the symbol. 相似文献
7.
LetM be a von Neumann algebra with a faithful normal tracial state and letH
be a finite maximal subdiagonal subalgebra ofM. LetH
2 be the closure ofH
in the noncommutative Lebesgue spaceL
2(M). We consider Toeplitz operators onH
2 whose symbol belong toM, and find that they possess several of the properties of Toeplitz operators onH
2(
) with symbol fromL
(
), including norm estimates, a Hartman-Wintner spectral inclusion theorem, and a characterisation of the weak* continuous linear functionals on the space of Toeplitz operators. 相似文献
8.
In the present work, necessary and sufficient conditions are given in terms of a nonnegative Borel measure which ensure the boundedness and compactness of operators with power-logarithmic kernels from L
p
(0, a) to L
p
(0, a) (or to L
q
(0, a)), where 0 < a < , 1 < p, q < , > 1/p and 0. 相似文献
9.
A. S. Romanyuk 《Ukrainian Mathematical Journal》1995,47(1):91-106
Order estimates are obtained for the best approximations of the classesB
1,
r
in the spaceL
q
with 1<q< and classesB
,
r
in a uniform metric. The behavior of Kolmogorov widths of the classesB
p,
r
,1<p, in the metric of L is studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 79–92, January, 1995. 相似文献
10.
It is shown that the algebra of the multipliers of the space p (1<<) contains the closed subalgebra Cp+H
p
, which coincides with the Douglas algebra C + H for =2. It is proved that a Toeplitz operator with symbol from Cp+H
p
is Fredholm on p if and only if its symbol is invertible in Cp+H
p
.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 124–128, 1987.The authors are grateful to V. I. Vasyunin for assistance. 相似文献
11.
Schatten class hankel operators on the Bergman space 总被引:1,自引:0,他引:1
Dechao Zheng 《Integral Equations and Operator Theory》1990,13(3):442-459
In this paper we characterize Hankel operatorsH
f andH
f on the Bergman spaces of bounded symmetric domains which are in the Schatten p-class for 2p< and f inL
2 using a Jordan algebra characterization of bounded symmetric domains and properties of the Bergman metric. 相似文献
12.
R. C. Smith 《Integral Equations and Operator Theory》1996,25(3):329-335
Invertible composition operators on the Hardy spaceH
p
have automorphic symbols. For 1<p< andp2 it is shown that some elliptic composition operators are scalar while others are generalized scalar but not spectral, that parabolic composition operators are generalized scalar but not spectral and that hyperbolic composition operators do not have the single-valued extension property. 相似文献
13.
N. M. Konsevich 《Ukrainian Mathematical Journal》2001,53(1):26-34
We obtain order estimates for the best orthogonal trigonometric approximations of classes of functions of many variables L
, p
in the space L
q, 1 < p < q < , q > 2. 相似文献
14.
We give a characterization of the weights u(·) and v(·) for which the fractional maximal operator M
s is bounded from the weighted Lebesgue spaces L
p(l
r, vdx) into L
q(l
r, udx) whenever 0 s < n, 1 < p, r < , and 1 q < . 相似文献
15.
Suzanne Lenhart 《Applied Mathematics and Optimization》1982,9(1):177-191
We show existence andW
loc
2,p
W1,-regularity results for the integro-differential equation, associated with a diffusion process with jumps on a bounded domain. The second order elliptic partial differential operator and the integral operator involved here are both maximum principle type operators, which enables us to makeW
1, a priori estimates. 相似文献
16.
A. B. Gulisashvili 《Journal of Mathematical Sciences》1985,31(1):2662-2672
It is proved in this paper that the characteristic function of the half-space is not a multiplier for the pair (B
pq
1/p
, B
p
1/p
), 1<p<, 1<q . In addition, necessary and sufficient conditions are found for the validity of the inclusion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 36–50, 1984. 相似文献
17.
G. V. Radzievskii 《Ukrainian Mathematical Journal》1994,46(3):290-303
For the equationL
0
x(t)+L
1x(t)+...+L
n
x
(n)(t)=O, whereL
k,k=0,1,...,n, are operators acting in a Banach space, we establish criteria for an arbitrary solutionx(t) to be zero provided that the following conditions are satisfied:x
(1–1) (a)=0, 1=1, ..., p, andx
(1–1) (b)=0, 1=1,...,q, for - <a< b< (the case of a finite segment) orx
(1–1) (a)=0, 1=1,...,p, under the assumption that a solutionx(t) is summable on the semiaxista with its firstn derivatives.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 279–292, March, 1994.This research was supported by the Ukrainian State Committee on Science and Technology. 相似文献
18.
The Grothendieck group K0() of the group of finite permutations of a countable set is described. All semifinite characters of are described and with their help the cone of representations K
+
0
() is characterized.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 123, pp. 126–151 (1983). 相似文献
19.
Liming Yang 《Integral Equations and Operator Theory》1996,25(3):373-376
Let 1<p< and
. LetC
q
denote the Bessel capacity in the plane. Let
be the set of homomorphisms ofH
(G) such that (z)= and letNP denote the set of points in G for which
is not a peak set forH
(G). In this note, we show that ifC
q
(NP)=0, thenH
(G) is dense inL
a
p
(G), the Bergman space overG.Partially supported by NSF DMS-9401234 相似文献
20.
Summary The existence of optimal nodes with preassigned multiplicities is proved for the Hardy spacesH
p
(1<p<). This is then used to show that the exact order of convergence for the optimal qudrature formula withN nodes (including multiplicity) is
where 1/p+1/q=1 and 1p. 相似文献