b and i tags not working in StyleableTextField for mobile development

Question

I'm trying to dynamically produce TextArea instances in a Flex mobile app that implement html formatting.  I've made a lot of progress, but simple <b> and <i> tags are not being rendered correctly. 
My current hypothesis is that I need to embed the italic and bold fonts.  I am currently not embedding fonts for these particular TextArea instances at all -- they are rendering using the system font.  In my previous experience, this eliminates problems with rendering <b> and <i> text.  However, when deploying on mobile platforms, I don't know for sure if there is a bold or italic system font natively available. 
If I need to embed the bold and italic fonts for the tags to process correctly, does anyone know which font(s) I should embed and how I should name them so that the html will be able to find them and render correctly?  I am applying a CSS to these TextArea instances in the full app, so I can do any font embedding there if necessary.  I am planning to compile this app for both iOS and Android, in case that makes a difference. 
Below is a simplified example of the code I'm using.  The TextArea that is generated is formatted honoring the <br /> tags, but ignoring the <b> and <i> tags. 
Thanks in advance for any help. 
import mx.events.FlexEvent;
import spark.components.TextArea;
import spark.components.supportClasses.StyleableTextField;
import spark.skins.mobile.TextAreaSkin;
protected function application1_creationCompleteHandler(event:FlexEvent):void
          var textArea0:TextArea = new TextArea();
          textArea0.setStyle("skinClass", TextAreaSkin);
          addElement(textArea0);
          var styleableTextField0:StyleableTextField = StyleableTextField(textArea0.textDisplay);
          styleableTextField0.multiline = true;
          styleableTextField0.htmlText = "<b>bold</b><br /><i>italic</i><br />normal";

Answer 1

Huh!  I tried tracing the htmlText property after formatting, and the bold and italic tags are not there anymore.  Unexpected, but consistent with the results.  Thanks for suggesting that test.  Here is the line where I assign the htmlText property:
styleableTextField0.htmlText = "normal<br/><i>italic</i><br/><b>bold</b><br/><a href='http://www.google.com/'>link</a>";
Here is the section where I create the StyleSheet and assign it to the StyleableTextField:
var styles:String =
  "@font-face{ fontFamily: Arial; src: url('assets/fonts/Arial.ttf'); embedAsCFF: false;}" +
  "@font-face{ fontFamily: Arial; src: url('assets/fonts/Arial Italic.ttf'); fontStyle: italic; embedAsCFF: false;}" +
  "@font-face{ fontFamily: Arial; src: url('assets/fonts/Arial Bold.ttf'); fontWeight: bold; embedAsCFF: false;}" +
  "a { color: #FFE043; textDecoration: underline; } " +
  "a:active{ color: #ffffff;}" +
  "b{fontWeight:bold; fontFamily: Arial;} " +
  "i{fontStyle:italic; fontFamily: Arial;}";
var myStyleSheet:StyleSheet = new StyleSheet();
myStyleSheet.parseCSS(styles);
styleableTextField0.styleSheet = myStyleSheet;
And here is the trace statement
trace( styleableTextField0.htmlText); // <TEXTFORMAT RIGHTMARGIN="21" INDENT="10" LEADING="2"><P ALIGN="LEFT"><FONT FACE="Arial" SIZE="16" COLOR="#FFFFFF" LETTERSPACING="0" KERNING="0">normal</FONT></P></TEXTFORMAT><TEXTFORMAT RIGHTMARGIN="21" INDENT="10" LEADING="2"><P ALIGN="LEFT"><FONT FACE="Arial" SIZE="16" COLOR="#FFFFFF" LETTERSPACING="0" KERNING="0">italic</FONT></P></TEXTFORMAT><TEXTFORMAT RIGHTMARGIN="21" INDENT="10" LEADING="2"><P ALIGN="LEFT"><FONT FACE="Arial" SIZE="16" COLOR="#FFFFFF" LETTERSPACING="0" KERNING="0">bold</FONT></P></TEXTFORMAT><TEXTFORMAT RIGHTMARGIN="21" INDENT="10" LEADING="2"><P ALIGN="LEFT"><FONT FACE="Arial" SIZE="16" COLOR="#FFFFFF" LETTERSPACING="0" KERNING="0"><A HREF="http://www.google.com/" TARGET="">link</A></FONT></P></TEXTFORMAT>
Lots of code modification going on behind the scenes, it would seem.  Any idea as to why the bold and italic tags are being stripped out when the formatting process happens?  Any idea of what steps I could take next?  Thanks for all your help so far! 
BTW, here's a screen capture of what the text looks like at this point: