An analog of Young’s inequality for convolutions of functions for general Morrey-type spaces

Triebel–Lizorkin–Morrey spaces and differences

“…Let 1 < 𝑝 ≤ 𝑢 < ∞ and 0 < 𝑞 ≤ ∞. Then there are two constants 𝐶 1 , 𝐶 2 > 0 independent of 𝑘 ∈ ℕ such that 2) .…”

“…Second at the end of step 1 from the proof of Theorem 2.1. in [24] Young's convolution inequality is used. But also in this case a counterpart for the Morrey case exists, see [2]. Everything else we have to change in the proof of Theorem 2.1. is obvious.$$\Box$$…”

Approximation in generalized Morrey spaces

“…The classical Young's inequality for convolutions with kernels in L 1 (R n ), known for L p -spaces, holds also for Morrey spaces. In a more general denition of Morrey spaces, Young's inequality was recently studied in [5]. Here we are interested in the preservation of the vanishing properties (V 0 ), (V ∞ ) and (V * ) by convolution operators.…”

Some properties of convolution in symmetric spaces and approximate identity

“…Basicity of the classical exponential system, as well as its perturbations in the subspaces of Morrey space of functions de…ned on [ ; ] was investigated in [6,11,13,15] by the method of boundary value problems for analytic functions on a complex domain. In [12,16,23], an analogue of the classical Young inequality and some properties of the convolution of periodic functions belonging to Morrey type spaces have been obtained. In [12], it was proved that the convolution in the subspace of Morrey space can be approximated by …nite linear combinations of shifts.…”