Bilinear Multipliers of Weighted Wiener Amalgam Spaces and Variable Exponent Wiener Amalgam Spaces

Abstract

Let [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.] be slowly increasing weight functions, and let [InlineEquation not available: see fulltext.] be any weight function on [InlineEquation not available: see fulltext.]. Assume that [InlineEquation not available: see fulltext.] is a bounded, measurable function on [InlineEquation not available: see fulltext.]. We define [Equation not available: see fulltext.] for all [InlineEquation not available: see fulltext.]. We say that [InlineEquation not available: see fulltext.] is a bilinear multiplier on [InlineEquation not available: see fulltext.] of type [InlineEquation not available: see fulltext.] if [InlineEquation not available: see fulltext.] is a bounded operator from [InlineEquation not available: see fulltext.] to [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.]. We denote by [InlineEquation not available: see fulltext.] the vector space of bilinear multipliers of type [InlineEquation not available: see fulltext.]. In the first section of this work, we investigate some properties of this space and we give some examples of these bilinear multipliers. In the second section, by using variable exponent Wiener amalgam spaces, we define the bilinear multipliers of type [InlineEquation not available: see fulltext.] from [InlineEquation not available: see fulltext.] to [InlineEquation not available: see fulltext.], where [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.] for all [InlineEquation not available: see fulltext.]. We denote by [InlineEquation not available: see fulltext.] the vector space of bilinear multipliers of type [InlineEquation not available: see fulltext.]. Similarly, we discuss some properties of this space. MSC:42A45, 42B15, 42B35. © 2014, Kulak and Gürkanl¿; licensee Springer.