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Some properties of the bilinear multiplier space on variable spaces were given by Kulak and Gürkanlı [18].
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This paper focuses on the design of a stable Lagrange multiplier space dedicated to enforce Dirichlet boundary conditions on embedded boundaries of any dimension.
A new algorithm is introduced to build a stable Lagrange multiplier space from the traces of the shape functions defined on the background mesh.
The regularity of weak solutions is examined by imposing some critical growth conditions only on the pressure field in the Lebesgue space, Morrey space, multiplier space, BMO space and Besov space, respectively (see [4]).
A mortar matching condition is enforced on the solutions across the subdomain interfaces by introducing a Lagrange multiplier space.
By using dual multiplier spaces [29] for the interpolation of λ one obtains a lumped matrix structure and, thus, the discrete multipliers can be explicitly eliminated.
We characterise the interpolating sequences for the Besov spaces Bp and for their multiplier spaces.
For instance, they are good substitutes of the ordinary Hardy spaces when considering the boundedness of non-translation invariant singular integral operators, they also appear in the characterization of multiplier on Hardy spaces and in the regularity theory for elliptic and parabolic equations in divergence form; see [21 23] for example.
Roughly speaking, in the linear case, by adding the condition that the Hardy-Littlewood maximal operator is bounded on weighted variable spaces, the results of multipliers on weighted variable spaces can be derived from the weighted multiplier theorem on classical Lebesgue spaces and the extrapolation theorem on weighted variable spaces.
And the one for multipliers on Lorentz spaces was given by Villarroya [[28], Proposition 3.1].
We investigate the boundedness of unimodular Fourier multipliers on modulation spaces.
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