Since you are doing an ajax request clearly the Redirect should have no effect. What you need to do instead is do it from the client-side, on the success
handler:
public void ProcessRequest(HttpContext context)
{
context.Response.ContentType = "text/plain";
string searchValue = context.Request["txtBoxValue"].ToString();
//Return the redirect URL instead
context.Response.Write("SearchResults.aspx?search=" + searchValue);
}
$.ajax({
url: 'Handlers/SearchContent.ashx',
data: { 'txtBoxValue': txtBoxValue },
success: function (data) {
window.location= data;//redirect here. "data" has the full URL
}
});
Now, if this is all you are doing in the ashx handler, I don't really see the need for the ajax request.