Sentence examples for boundedness for the operator from inspiring English sources

Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents.

In this paper, the boundedness for the operator on the product of homogeneous Morrey-Herz spaces in nonhomogeneous setting is found.

In the case for, we will use the weak homogeneous Morrey-Herz spaces and weak homogeneous Herz spaces to derive the following boundedness for the operator.

First, we establish a sharp estimate for the operator T b ; and second, we prove the boundedness for the operator on L p spaces with variable exponent by using the sharp estimate.

In this paper, we establish the boundedness for the operator T ∗ and its commutator on the weighted Morrey spaces L α, V, ω p, λ ( R n ) related to certain nonnegative potentials belonging to the reverse Hölder class B q for n / 2 ≤ q < n, where p 0 ′ < p < ∞ and 1 p 0 = 1 q − 1 n.

Motivated by these papers, the main purpose of this paper is to introduce some Toeplitz type operator related to some singular integral operator satisfying a variant of Hörmander's condition and prove the boundedness for the operator on L p spaces with variable exponent by using a sharp estimate of the operator.

In [6 8], some Toeplitz-type operators associated to the singular integral operators and strongly singular integral operators were introduced, and the boundedness for the operators was obtained.

In [10, 11], some singular integral operators with non-smooth kernel are introduced, and the boundedness for the operators and their commutators are obtained (see [9, 12 16]).

In [12, 13], some singular integral operators with non-smooth kernels are introduced, and the boundedness for the operators and their commutators is obtained (see [14 17]).

In [6], some singular integral operators satisfying a variant of Hörmander's condition are introduced, and the boundedness for the operators is obtained (see [6], [20]).

In [5, 6], some singular integral operators satisfying a variant of Hörmander's condition and the boundedness for the operators and their commutators are obtained (see [6]).